I don't think separate browsers is a very effective mitigation. If both browsers are running on the same machine, from the same ip address, using the same email address for logins, the same phone number for 2FA, it will be pretty clear that both browsers represent the same person. Even cross-device identity tracking is a real thing.
In general you shouldn't be logging in to any of the "fun" sites. If you do, you should create a burner email address and separate logins (and obviously separate passwords) for each site. A lot of the "fun" Internet doesn't require 2FA, but for sites that do (which is an increasing number of social media providers), I'd highly recommend getting a Google Voice number and using that. That shifts the trust boundary to Google, who is going to have all your info anyway, rather than dozens of fly-by-night websites.
If the definition of "fun" sites doesn't even include anything with a login (no youtube, no forums, no HN...), then it feels like it includes so little as to be meaningless. The "business" internet (at least most of it) needs to be anonymous if we want to have a free society and efficient markets.
