If it was originally built using a framework, what framework do you think that would be? And would it still be in active development and evolving today? How do you integrate new code in a legacy or evolving framework? My experience of this says it is not really a framework vs no-framework problem, but a problem of how to keep an applications code base healthy in a world of ever changing and evolving features, developers, frameworks and technologies. I think thats the real problem you are dealing with here, and not "hot-shot developer from 10 years back didn't use the coolest stack of that time".
And it is the problem you were hired to solve. If everything was working perfectly with no new features required to be added to the legacy code base, they simply wouldn't need you.
Angular was bad and it's ashamed that it's hype pretty much relegated better toolkits like Dojo and MooTools to the dustbin of history.
While React has lots of great ideas, good marketing and the facebook brand is really what boosted its popularity. Popular does not necessarily mean great. There must be some other great homegrown frameworks out there, but we have never heard of them, since they did not start out as a facebook or google homegrown framework.
> it seems that Facebook really grasped early on what was happening with React,
This just is not accurate. React has also evolved a lot since its inception, they've just been careful about maintaining backwards compatibility compared to angular.
I googled/linkedin developers that have worked on this codebase for the past decade and most of them appear to have this "rockstar developer" thing going on. They are opinionated, had heated debates (from what I'm told), and often rolled their own solutions whenever possible. Now we see the result of these geniuses doing their thing.
Just use a framework please, your homegrown solution is sucks. I guarantee it.