Odd: apt search “.*bleachbit.*” finds only a single entry:
$ sudo apt search '.*bleachbit.*' Sorting... Done Full Text Search... Done bleachbit/amber 2.0-3 all delete unnecessary files from the system
… so I wonder where the store is finding “BleachBit (as root)”. Anyway, after “sudo apt install bleachbit”, I too see both regular & root versions in the App Drawer, and like you I found the root version never launched. Digging a bit:
$ grep '^Exec=' /usr/share/applications/bleachbit* /usr/share/applications/bleachbit-root.desktop:Exec=pkexec bleachbit /usr/share/applications/bleachbit.desktop:Exec=bleachbit
When I open a terminal & run “bleachbit”, it works fine, but with “pkexec bleachbit”, a GUI password prompt (for user “purism”) is presented, and my login credential is accepted, but it nevertheless errors out with “Could not open X display”. Setting environment variables WAYLAND_DISPLAY=wayland-0 and DISPLAY=:0 does not change anything. I get the same error with “sudo bleachbit”, but that’s no surprise: https://bugzilla.redhat.com/show_bug.cgi?id=1274451#c33 says “there are currently no plans to support running graphical apps with sudo under Wayland, and it seems quite unlikely that this will change anytime soon”.