Does Epiphany/Web support profiles, and if so, where should they be stored?

Question

Previously in Epiphany/Web, you could launch different profiles in new instances using the --profile flag, similar to Firefox. This was handy if, for example, you wanted a separate instance using a different Google/Firefox Sync account. But everything changed when the Fire Nation attacked elementary switched to Flatpaks, and this doesn't work any more.

Installing epiphany-browser via apt and doing epiphany-browser --profile="/home/USER/.local/share/epiphany/PROFILE" works. However, using the preinstalled version with flatpak run org.gnome.Epiphany --profile="/home/USER/.local/share/epiphany/PROFILE" (or the longer version I found in the .desktop file, /usr/bin/flatpak run --branch=daily --arch=x86_64 --command=epiphany org.gnome.Epiphany) doesn't work; it just launches an incognito window.

Is there a way to get profiles to work in the Flatpak version of Epiphany/Web? Do they need to be stored in any particular place?

edit: Figured it out myself, the solution is to go into System Settings→Applications→Permissions and give Gnome Web access to Home & System folders! Leaving this here in case anyone else has this problem. As per Michael C.'s answer, it only needs access to Home, and profiles are stored in ~/.var/app/org.gnome.Epiphany.

Answer 1

edit: Figured it out myself, the solution is to go into System Settings→Applications→Permissions and give Gnome Web access to Home & System folders! Leaving this here in case anyone else has this problem.

Well that will work, but it's not safe. This is a web browser, you don't want it to have unlimited system access. The equivalent of ~/.local/share/epiphany under flatpak is ~/.var/app/org.gnome.Epiphany/data/epiphany, so you can just move your profiles there and not worry about giving it extra permissions. Have fun.