I log into my personal gmail and Facebook on Firefox and everything else on Chrome. I’ve been doing this for years now and I’m perfectly comfortable. For the most part I’ve forgotten about any differences between the two browsers.
If this is your strategy, you're going to also need to avoid google documents and signing into youtube.. and there's also the fact that at some point you need to ask yourself if Chrome is really great enough to warrant using multiple browsers when Firefox containers take care of everything privacy related for you.
Using Brave for a bit will give you some perspective on what sort of things (e.g. location) are being requested whenever you hit a Google-related page.