I have a 16 with iOS 27.0.1, and searches work fine for me. Are you running any VPNs, anti-virus, or "cleaner" apps? Anything with system wide access that includes Photos?
- Do you have “Optimize Storage” checked in Settings>[name]>iCloud>Photos
- Do you see all your iPhone pictures at iCloud.com?
- What is your storage in iCloud? At Settings>[name]>iCloud>Storage, mine says 166.6 GB of 200 GB used. What does yours say?
- What is your storage on this iPhone? At Settings>General>iPhone Storage, my phone says 50.5 GB of 128 GB used. What does yours say?
Have you tried a forced re-start of the phone?
Force restart iPhone - Apple Support
This is different from a simple Power Off. For me, the logo appears 5 or 10 seconds past the "slide to power off" message. Wait for the logo; don't do the slide thing.
Why are you using iCloud? See this:
Understanding iCloud Photos - Apple Community