I know its antithetical to Flatpak sandboxing, but I genuinely spent hours trying to move a non-Flatpak profile to flatpak and gave up. I gave the Flatpak filesystem permissions and then it would use the usual ~/.firefox folder, even if it says it doesn’t in about:profiles.
I can’t explain why any of this works the way it does but it appears that Firefox is just very confused about profiles when it exists in a Flatpak container.
Well if they ever pull another “you must use snap or die”, you’ll have to imagine it. Thankfully, this exists https://github.com/acmesh-official/acme.sh