It is interesting to think how SEGA had almost everything going for them potentially and how they seemed to screw it up again and again.
As with most things SEGA the main issue was the Japanese and USA branches civil war and struggle for power. Pretty much doomed the company.
SEGA Japan had the development and engineering talent while SEGA USA had the marketing know how and good relations with western developers.
The problem was that the USA branch had caught lightning in a bottle with the Megadrive release there and to also Europe as SEGA Europe back then was mainly just for distribution they didn't really make any big decisions.
The overall management looked at the relatively poor performance of the Megadrive in Japan who were facing an entrenched Nintendo with incredible brand presence and some dodgy protectionist practices keeping them well in the lead.
Japanese branch was likely getting compared unfavorably to the massive success abroad and so the rivalry ensued.
If the company had looked at things from a worldwide perspective and worked towards a single common goal most of the bullshittery that followed could have been avoided. That's the first thing that would need to have been fixed for this alternate timeline to play out.
I think releasing the Mega CD was a fine idea at the time and it was a serviceable add on, after all Nintendo was also looking into similar solutions so I don't really count this among their massive blunders but it certainly didn't set the world on fire and possibly should have been Japan only but again....at the time CD was going to be the big this so can't fault them too much.
Cutting support for the Megadrive was an absolutely terrible idea. Again mostly a pride thing from the Japanese branch as they finally felt that had something in the works that would be popular in their home market (Saturn) and thus didn't want to split their resources and wanted to focus only on the Saturn.
This allowed Nintendo to gain back a lot of ground in the US market towards the end of the 16-bit era (1994 - 1996). This also added to a narrative that SEGA don't support their hardware and will abandon on a whim. If SEGA had kept strongly supporting the Megadrive the way Sony/MS/Nintendo do in the transition phase/end tail of a consoles life then we could be looking at a very different course in the timeline, especially they wouldn't have lost mindshare in the marketplace and would have continued earning massive profits from Megadrive sales/software.
The next thing would be the stupid add ons. 32X should simply not have existed. The money that was wasted on R&D, production and marketing plus the development of games etc... could have been put to much better use within the company at large. The main reason for it again was the US/Japan tug of war. The Japanese branch wanted to stop focusing on Megadrive and go with their new baby but the US wanted to keep the "Genesis" brand going as it was a big success for them. If the 32X doesn't happen due to the above two points in this timeline being fixed then SEGA doesn't loose more money, mindshare and reputation in the market and whole company is focused on a single goal of success.
Add to this things like Nomad which shouldn't have existed, let's take those things out of the picture for this "better" timeline to exist. More money and reputation saved.
So far in this timeline we have a united SEGA working with great synergy and togetherness towards the single goal of worldwide success. We have a long supported Megadrive with some marketing push still behind it and more late gen releases. We have no bullshitty add-ons costing money and reputation in the market and we have a slightly weaker Nintendo in the market due to actually having competition in the tail end of the 16-bit era.
So this could potentially set up SEGA to be in a good position going into the 32-bit era.
Now it seems pretty obvious that the future was going to be 3D. Here's the thing SEGA were pretty much the pioneers for 3D gaming with their arcade business, they had created spectacle arcade experiences that wowed everyone. First 3D Fighter, Racing etc..
SEGA actually approached Lockheed Martin if I'm remembering correctly because they wanted to license their 3D flight simulator technology, or at least a cheaper version obviously. SEGA were ahead of the game in this field, you could say that at the time they had the strongest video game 3D development experience/understanding in the world at the time.
They should have leveraged this into their next home console and made the Saturn a 3D beast. The reasons for not doing this seem mostly to be a fear of cannibalizing their arcade business. "Why go to the arcade if they can get it at home?". Obviously it was a terrible read of the market to concentrate on a 2D first console at the time but I think even they could read the signs but the arcade business came first and their hope was to continue a 2 tiered system where arcades where like an "experience" where you saw the marvels of technology and home market was simpler games. Kind of like those analogies you see about the Cinema experience vs home video on a small CRT.
I can't stress enough how far ahead they should have been on this and how important it was at the time but how they dropped the ball hard. Almost makes my brain hurt.
Anyway to change the course of the timeline if they had focused on the start at making a powerhouse 3D console in the Saturn from the beginning which would also make it much easier to develop for things would have been very different.
Taking the other points of this timeline into account if SEGA come out of the 16-bit era strong and without the BS infighting if they go this route with the Saturn things are looking potentially very good for them. Megadrive still being supported for the early transition years to the 32-bit era. Nintendo still launching really late with N64 exactly as it is, Cartridges an all.
At the time lots of companies were fed up of Nintendo's shit policies and treatment of them and were looking for any excuse to get away from them, Nintendo launching late and going with carts rather than CDs helped seal that deal.
Even in our time line SEGA were making great headway in Japan and with Japanese developers. Like many had said Resident Evil, Tomb Raider etc... were originally going to be Saturn exclusives, even Final Fantasy VII was aiming for Saturn. So taking all of this into account with a non fumbled 16-bit tail era and strong foundation for the 32-Bit era things could have been very very different for the "new" timeline.
Now Sony were certainly no slouch, their marketing was amazing. They had the money to back up their play into gaming, they had solid hardware and they were offering a way out from Nintendo's grip and also the ability to not compete with the amazing first parties of SEGA and Nintendo, to have the spotlight. Definitely enticing for developers.
Also they were willing to co-fund development, assist with marketing or even pay for all marketing in some cases. Hard to refuse from a dev stand point.
Having said that in our timeline SEGA basically handed them their ball and the whole marker due to all of their blunders so these once Saturn games all because Playstation landmarks instead. But in the new timeline with a strong SEGA with a 3D focused Saturn launched on time and with good pricing it is very possible that Sony could have been ignored in the maket by the hardcore for someone they know and again the developers could have chosen to make most of those games Saturn exclusives.
So it's possible Sony could have fumbled with their foray into gaming and quickly disappeared like some before them. The Saturn could have essentially become the Playstation in terms of dominance, or maybe a slight less successful one without Sony's marketing prowess/financial backing.
Of course the market could have split more evenly with some developers such as Namco and others going mostly Sony and others going mostly Sega. With this Sony has their foot in the door with a solid contender but don't become the phenomenon that Playstation became and SEGA have a strong market presence with the Saturn, possibly leading the generation. This all assumes Nintendo goes exactly as they did in the real timeline so no specific changes there, N64 still launches late with cartridges and sells around the same it did originally.
It's important to note that this Saturn has a wildly successful Shenmue that's marked as a landmark title and system seller. The story completes etc... tons of great ports of things like Virtua Fighter, Sega Rally which actually become successful this time and are competent ports, plus other SEGA games that never existed that would likely have been developed become a strong Saturn library along with likely the lionshare of games that we know now as "Playstation" games.
Also as others have said, have a strong 3D Sonic game early in Saturn's life. This makes a huge difference to the market.
Obviously in this new timeline there is no Dreamcast as the Saturn was a successful generation.
After that it's pretty much impossible to tell where things could go as the timelines would diverge far too much to be able to predict anything. Would PS2 have still been a thing? Would it have been the phenomenon it was? Would Nintendo still make Gamecube? Would there be a Saturn 2? Would Microsoft buy SEGA? Would there still be an Xbox if they didn't?
Just too hard to tell but a fun hypothetical. SEGA had the opportunity to make that timeline a reality or at least elements of it in some form but they dropped the ball hard like nobody has ever done before. SEGA really is their own worst enemy. The main thing to take from it was the in fighting rivalry. Nothing else in the timeline happens unless that gets fixed as it's literally the crux of everything else. Looking at it like that it's pretty clear to pinpoint that as the main reasons for SEGA becoming what they did.