I'll detail my solved issue here, and an ongoing one.
My first issue was trying to get my external HDD from my PS4 to work with the PS5. The drive was working perfectly on the PS4 to start. On initial plugin to the PS5, the system said it was corrupted. Couldn't see the drive/games at all. Booted the PS4 back up, plugged in the drive, and lo and behold, it had become corrupted. The PS4 was able to repair it, all games came back, good to go. Replugged it into the PS5. This time, the games showed in my library, but the entire PS5 slowed down. Could still not see the drive in the external storage system setting. A bunch of random games start going in the download queue, for patches. During this, numerous games show as No Title in the download queue, and when these games finish downloading, 90% of them pop up saying Unknown completed downloading. I leave the PS5 alone, and it seems it sorted it self out. I was able to see the external HDD (takes a few minutes to show though), and all my games are in my library, displaying correctly and able to be played.
However, due to this, or maybe another issue, I still have any PS4/cross-gen game pop up as Unknown when downloading is completed/installed.
It seems to be fine now, but I have unplugged it just in case due to issues I've been seeing online about externals.