@lamy if it works on XFCE it should work on Gnome. Gnome has the best integrated support for fingerprint readers as far as the DE itself goes. If a distro is using an up to date version of fprintd it shoudl simply work as long as the fingerprint reader is enabled in the UEFI/BIOS. fprint - ArchWiki
I used Manjaro Xfce for the first nine months with my Framework, and then switched to Fedora with GNOME for the past five months. My recommendation is to use GNOME. Manjaro’s GNOME edition should be fine. Getting the fingerprint reader to work, and getting the display settings right for Framework’s 2256x1504 display, was not entirely smooth in Xfce.