How does it not fit the era? We know almost nothing about federation starship design of that era, we've seen the constitution class and that's it and by the time of The Cage the Enterprise was already supposed to be an older ship with a history.
Discovery could easily be 20 years older or younger than the constitution class to explain the differences and let's be honest, starfleet changes its design elements all the time. Look at the movie era, connie refit, exclesior and oberth all have completely different nacelles, saucer shapes, secondary hulls.
It's the same in the 24th century, the enterprise d, defiant, voyager and enterprise e were all build within a few years and look nothing alike (and excelsiors, oberths and mirandas are still flying making them contemporaries of 24th century ships too).
So what? There isn't always a clear evolution in design, B doesn't have to look like an intermediate step between A and C.
I mentioned the Oberth class above, how does that fit the designs that came before and after?
Let's look at some Volkswagens:
1960s:
1990s:
2010s:
Does the middle one look like it fits between the others? Not really, it still happened.