I’m experiencing this too, and I found this article with a suggestion that worked: https://www.idownloadblog.com/2023/04/07/how-to-fix-slow-search-on-iphone/
Toggle Search off and on
- Go to iPhone Settings and tap Siri & Search.
- Scroll down and turn off all the switches you see in the screenshot below.
- Restart your iPhone.
- Go back to Siri & Search settingsand turn on the switches. After this, Spotlight Search should work as intended.
This makes sense that it works because after an OS update, Siri updates its search index for your phone messages, mail, and apps. It can take a long time and while it’s working in the background, apps slow down and searching can take longer than usual, and you might notice Photos.app says that it’s not syncing to iCloud because it is “optimizing system performance.” To help it along, I also made sure to turn off low power mode and plug in my phone so that the phone can run these long tasks as quickly as possible.