Can somebody confirm if somehow its possible to install hardware acceleration on Fedora and Manjaro (with and without Intel drivers)? And how to do it?
In general information for archlinux should work on Manjaro, that being said some things may be Manjaro specific, in which case search their documentation or follow the guides on the Framework website.
For general suggestions on the laptop with archlinux distros you can also look here Framework Laptop - ArchWiki
Any hardware acceleration on the Framework for browsers will require the use of intel drivers, no way around that.