No default browser works normally but no idea how to set that in Hyprland.
I highly advise against Appimages. Flatpak is only useful if you dont trust the app which is a valid opinion, but poorly then the browser cant sandbox websites on its own. So native packages are the best option for security it you trust the browser.
Perfect would be to have the browser isolated and also using its sandbox to isolate websites from each other. I dont know if this works though, on Android it does (not with Firefox poorly as they didnt implement it)