To address the search concern, after updating your iPhone has to reindex all of your data and files for search, which is creating and sorting a searchable database of your data. Give it a few days, best when connected to a charger and on Wi-Fi as most of the indexing is done then, and little by little search results should load back.
To address the touch, first try a Forced Restart.
- Press and quickly release the Volume Up Button
- Press and quickly release the Volume Down Button
- Press and hold the Side Button until you see the Apple Logo.
Then check your battery health in Settings > Battery > Battery Health and Charging.
If the percent is below 80% or the Forced Restart doesn't work, have it serviced at your Genius Bar.
Genius Bar Reservation and Apple Support Options - Apple