If you had a 4K monitor, the 4080 wouldn't be such a terrible choice. At 1440p however, you'll be heavily CPU-bound and that 9700K will hold it back massively to the point that you'd effectively be wasting your money on the 4080.
If you go the route of upgrading everything besides the CPU, you won't get much better gaming performance because that 3070 Ti is just about tapped out at 1440p.
Ocean Dweller
I had a very similar dilemma to you 8 months ago.
My old system was:
i9-9900K
RTX 2080 Ti
16GB DDR4 3200MHz
ASUS ROG Maximum Hero XI
Acer Predator x34p 3440x1440 120Hz
Samsung Evo 970 Pro 1TB
Overall, extremely similar in performance to your system and I was debating whether upgrading to a 13900K+DDR5 or getting a 4090 because I only had saved up enough for one of them. I ended up getting the 4090 and regretted it. My frame times were horrendous in modern games at ultra settings and I was suffering from extreme CPU bottlenecks that caused my 4090K to at times perform only 10-30% better than my 2080 Ti. I quickly decided to upgrade the entire system and was much happier for it. My performance more than doubled except for scenarios in which I hit the max refresh rate of my monitor and the smoothness was incomparably superior.
tl;dr, don't cheap out. Upgrade the entire system. You'll regret it and be wasting your money if you go one route or the other.
Edit: OP, I know you're salivating at those 4080 benchmarks but you must remain strong. You need a new system to allow it to stretch its legs. It'll be sleeping with a 9700K stifling its true power.