Photos App does not show in search
Spotlight uses a system process to index all files on the storage, so if you have a corrupt search or the process is crashing, the only true fix is to back up the device and erase/reinstall it if it's not a setting you can toggle.
That setting would be in the settings app - navigate to Siri & Search and then below the main settings is an alphabetical list of apps.
Toggle off all the photos items and then power down the phone. Then power it up and navigate back to re-enable them.
If after 30 minutes on charge, the index isn't working you'll want to prepare to erase and wipe the device.
If you are hesitant to do that (since you have to unync an Apple watch - get your health data on the iOS device - then back that up securely, then wipe and restore and then set up things like wallet, fingerprint if the restore doesn't work perfectly) you might try some other things.
- Reset all settings on the iOS device
- Consider asking Apple Care if there's anything else we missed or a known issue in your version of iOS.
If the version of iOS you're running has a bug, no amount of fiddling will fix that and you'll have to wait for a patch to apply.