The PS5 appears to be suffering from a bug that prevents players from downloading their games.
Reports of the 'Queued for Download' bug have surfaced over the weekend, and they claim the glitch prevents games and apps from being fully downloaded. The bug appears to show up when a game or app is first downloaded, but there are two different forms that it can take. The first is that the software will be perpetually "Queued for Download," and the second will provide a download error message. Either way, you'll be directed to the Downloads menu, but your game won't be there.
Since the error doesn't acknowledge that the download is happening, you won't be able to cancel your install and start again. According to IGN (opens in new tab), the software will show up in your library to confirm you own it, but the PS5 store will state the opposite, asking players to purchase games and apps they already own.
It's not clear exactly what causes the error to surface - a number of PS5 launch games and apps, from Demon's Souls to Disney+, have triggered the issue - but Call of Duty: Black Ops Cold War appears to be a particularly notable offender. There's no official word from Sony at this point, but Activision has reportedly encouraged players to perform a factory reset on their new consoles, a solution that, while inelegant and likely frustrating, does appear to be working. Hopefully we'll get a fix relatively soon, but until then it looks like you'll probably need to start those downloads from scratch.