UBlock origin adblocker is probably all most people realistically need

Use the facebook container extension on firefox so your session is isolated from the rest of your browsing. Also look up guides to harden firefox.

Use them in a separate Browser with Ublock origin.

Like everyone else said. You're pretty much fighting against tracking cookies at this point. My 2 cents. "Hardened" Firefox running containers for personal, shopping and that stiff. uBlock origin, Privacy Badger by the EFF and look up user-agent spoofing. Set your user-agent to something like Windows 11 chrome. If you're feeling adventurous look into a pi-hole as well.

You can use both through the browser, which is the safest way of doing things because the browser sandboxes the web apps, isolating them from your system. If you prefer an app for Messenger, look on Flathub, though I advise against it. The two apps I found for Messenger are Franz and Ferdium (a fork of Franz with more features).

To mitigate the privacy risks:

• Firefox with uBlock Origin (or Librewolf)
• Avoid sharing anything sensitive.

Nothing much you can do sadly.

I think that primarily third-party cookies are the most problematic thing when browsing the web, they use that crap to track you across sites and use it for ad targeting and "dynamic pricing". Yeah, uBlock Origin will deal with most of it, but Google/Amazon/Meta/X are very aggressive, so I’d consider using different browsers for different activities, and having a more secure browser if you are dealing directly with Facebook and Google accs, something like Mullvad if you can get used to the default screen letterboxing. This, with the cookie purging, will help you avoid theirs and others' cross-site tracking - just remember that not saving cookies means you are going to unlog from the sites every time you close the browser.
My main browser for daily, relaxed stuff is LibreWolf. I set cookie exceptions for sites I want to stay logged (like Lemmy). Some stuff doesn’t work correctly on LibreWolf because of some stuff it purged from FireFox, so you can go and do some manual configuration to harden regular Firefox and use for streaming and such, can also use it with Chameleon addon to give you a different signature from when you are using the other browsers. You can also change your VPN location when you are using each browser, so one more thing to make you look like a different user for each and make it less likely to have your different activities linked together.
If you are more tech-savvy, try ungoogled-chromium, but it requires a lot of manual setup.