Thank you, Jonas. I don't know how I missed that thread when I was looking, sorry! Also, my browser is Firefox.
After reading more, would upgrading my OS from Mint 21.3 to Mint 22 likely mean I don't have any of these issues in the first place? Or installing using something other than flatpak? I don't particularly mind what method I use to install/run it.
And more information on the things I tried/looked at, below for more context/information (if relevant)
I don't have anything for strawberry at /usr/share/applications/strawberry.desktop
sudo find /usr -type f -name 'strawberry' returns nothing
xdg-open tidal://test does nothing. However, flatpak run org.strawberrymusicplayer.strawberry tidal://test does add tidal://test.
(My understanding is all this is expected if one installed via flatpak?)
I ran some commands to create a wrapper script/desktop handler (I didn't write any of it; I'm not an expert on this stuff). After doing that, xdg-open "tidal://test" started working and would add it to the playlist, but I would run into the same SSL handshake error that others are posting in other threads. I undid those commands after because they hadn’t solved the problem.