Epiphany is "GNOME Web": https://apps.gnome.org/Epiphany/
On my Fedora 44 workstation, Firefox 151.0.1 has no problem raising its window to open links clicked from Thunderbird 149.0.1 (not even the latest version) on GNOME 50.1 with no extensions and Firefox set as the default browser.
https://snapcraft.io/thunderbird defaults to a much older version, 140.11… BTW I'd recommend ditching snaps and using flatpaks from flathub, i.e. the cross-distro standard that everybody other than Ubuntu is using.