If you’re using GNOME or a derivative, you should probably be using gio mount to do the same mounting as the file manager would. Then again, you say that the file manager isn’t working, so gio mount probably won’t work either.

I admit I had no idea about the guts of this - and maybe still don’t - but the user who suggested looking at udisks is probably right. It’s always been there in the background as long as I remember (Mint/Cinnamon, many years), and has hooks into something I mounted with gio after the last reboot.

Another search term that might help is “gvfs”, or GNOME virtual file system, which I’ve definitely poked around with before.

Importantly, Nautilus and gio don’t need sudo because they call into what’s already running. They (or the subsystem) automatically create the mount point directory (and remove it on unmount). If the directory already exists, they use the “append a 1” technique you experienced, presumably so they don’t clobber or hide something that might be important.