Sounds like some background process gets stuck in a crash-relaunch loop. Could be something you installed, could be a corrupt file somewhere, could be failing hardware, etc. It'll be hard for anyone to help debug this over the internet since there are so many variables involved. You need to narrow down the possibilities, so start with all the usual first order troubleshooting steps:
- If you're jailbroken, turn off all your tweaks and boot into 'safe mode' and see if it goes away.
- Uninstall any other stuff that might be related (swype, gboard, etc) and see if it goes away.
- Go to general > reset and 'reset all settings' and see if it goes away.
- Go to general > reset and 'erase all content' and see if it goes away (make sure you have a backup first)
- Do a full DFU wipe/reinstall and set the phone up as new WITHOUT restoring from a backup or logging into iCloud/AppleID, and see if it goes away.
iOS 13 is pretty buggy and lots of people have been having issues, but it's mostly been related to murdering battery life and apps randomly quitting for no reason. I haven't really noticed anyone complaining about search/keyboard issues yet.