Why are my apps not appearing after download on iPhone?

Every time I download an app from the App Store, it goes through the usual enter password, success chime sound, then nothing happens. No app anywhere. Not in library, not on any page, not in search. It’s like it was never downloaded, even though there was a success chime. Multiple different apps, all unpaid, new phone w lots of storage. Any ideas?!

[Re-Titled by Moderator]