I use a matrix server with a Facebook messenger bridge. The only thing it can't do is start new messages, so I still have to go to the site for that, but it's not that big of a hassle.
F-Droid
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
Matrix space | forum | IRC
SlimSocial for Facebook in the F-Droid store seems to have one - but I haven't tried it myself.
Maybe beeper too. If you self-host it.
Take a look at caprine: https://github.com/sindresorhus/caprine
There's no version for Android though, is there?
No, unfortunately, which is why I deleted the original message:(
I use fb in a work profile in brave and desktop mode. there u can access messenger. its a bit of a pain but it works.
I use Simple - Social Browser - https://play.google.com/store/apps/details?id=com.creativetrends.simple.app