right now my whole website is hilariously one giant PHP file (CSS and Javascript both embedded, lol), with a giant switch branch on the after-the-domain part of $_SERVER['REQUEST_URI'] (there's only a few branches because the landing page is the main bulk of the site). the website was rapidly prototyped, and I hadn't used PHP since like 2008. I don't have any interest in overly-complex ways of doing things (using classes for everything, using the MVC pattern), but I do want slightly better organization. I had to monkey-patch in some rudimentary caching on the database-intensive landing page when we started getting lots of traffic, and anything that would make that easier as I add more functionality (that also should be cached) to the site would be great.
oh, and I'm running the whole thing on IONOS shared hosting and for business reasons it's not really feasible to use anything else at the moment.
so this is why I'm looking at evaluating F3 or any other similar "minimalist" frameworks—I don't want or need a super opinionated complex rejiggering of my existing code, but some small amount of better formal structure would be nice.
also, I'm not using any other packages or libraries or anything, except for Stripe, which was incredibly easy to integrate.
Apart from that, I would skip framework if I were you. Web is littered with abandoned PHP frameworks which were all viable at some time. If it already works, just clean it up, refactor as needed and identify + resolve any performance bottlenecks.