How to recover missing photos and videos from iPhone 14 Plus?

It sounds like you ran out of room--if you don't have room to put stuff in, then you don't have any place to look, really. You can see this:

         If you're missing photos or videos in the Photos app - Apple Support

Basically the above says to look in Recently Deleted and in Hidden, which you may have already done. Be sure to check your Library thoroughly-- the pictures may not be where you expect, as dates may have changed. You can use the search field with the date or location. And remember, you can sort the Library by date captured or by date added.

If you have Settings>Apple ID>iCloud Backup turned on, then you may be able to recover some data from the last 30 days or so at iCloud.com, but you would need to look at the date of the backup to be sure it's from before you lost the images. iCloud Backup only works for pictures not stored in iCloud Photos. You should look here:

         View and manage iCloud device backups - Apple Support

This requires you to erase everything on your phone and replace it with the backup.

If you don't keep your own backups to an external drive, then there really isn't any place else to look.