I apologise if I'm missing something obvious here, but I've looked at a few different options around the OS, and nothing seems to work in this situation.
I think how the system manages installed games needs significant improvement. Maybe it's just a weird situation I've encountered, but the way the system tracks and manges where games are installed seems unfinished.
Having read the LTTP Earth Defense Force 5 thread, I decided I wanted to try the series, so I searched the PS Store for it. I discovered I'd apparently purchased EDF 4.1 at some point, so I decided to try and download that. Looking at the game on PS5, there's a "Play Game" button. I click it. "We can't find the storage device this is installed on.". Okay - I assume it's an external drive which is connected to the PS4 elsewhere in the house at the moment.
The message tells me to delete the game and re-download it if I want to. Great - I want it on the SSD anyway, so I'll just do that. Except - the popup offers no option to delete the game. I look at the menu options for the game to see if I can delete it from there. Nothing. At this point, why does it not just ask if I want to install it on the console, and download it to console storage? I got to the product page and saw a "Stream" button for PS Now, so it's possible I "own" it through that instead. I go to the PS Now section, find the game and press Download. I get a helpful "Something went wrong" error.
Okay - time to check my library and delete it from there. I go to my library, sort alphabetically and look under the letter E. Nothing. No mention of EDF at all. (Edit: Checked again and it is listed in the library, but there's still no delete option, so we're back to square one). Well, I think, it must be listed under applications in system settings then. Except, it's not. That only lists console storage, and doesn't list external games because the external drive isn't connected.
So what appears to have happened is the PS5's database says the game is installed on an external drive, which it may well be. Except, since the drive isn't connected, it removes all mention of the game from anywhere else in the OS. From what I could see there is no way to delete it, or delete this "link" it has created in the database. You also can't install it on another drive, for some reason.
Yes - the 'fix' here is for me to connect the external HDD, but that's not my point. What if that drive had broken or had to be formatted? The game is just forever unplayable because it can't be found and deleted? If the system is going to track that games are installed on external drives when they aren't connected, then it should offer a way to "uninstall" (remove that record it's created) so that the game can be installed on internal storage (or another connected drive) - or, the simpler option, it should just ignore that if the drive isn't connected, and let me install it somewhere else. As it is, the game is effectively "stuck" in an unplayable state and can't be accessed.
Edit: Well... I 'fixed' it. Someone on Reddit mentioned that sometimes external games would have content in console storage, and that needed to be deleted. Went to storage, and found a ~10mb "console storage exclusive" file for the game. Deleted that, and now it's downloading. That was confusing. I still think that process needs to be far more user friendly - ideally just have a "redownload game" button on the popup message.
