IOS 15.2 update didn't work, and it won't let me try again

I tried updating from ios 12.4 to 15.2 on my iPhone 8 plus, but it seems to have not worked.

The download has completed, but the settings still say that it's the older ios, and certain apps still won't let me update because they require a more recent ios. There's also still an update notification in my settings menu.

However, I'm not able to retry the update; The "install now" button is greyed out, as you might expect if the phone was already updated. I've already tried turning the phone off and on, and I'm not sure what else to do here.