Same issue, updated recently to 23H2 and now I cannot type in the Search box in the start menu or task bar.
Have tried restarting Windows Search, running the ctfmon program, changing menu alignment, etc. Nothing has fixed this.
Real pain and wasting a LOT of time now trying to find things in the meu where I could normally just type...
Update: I found a post with this info that seems to have fixed it for me, finally!
Method 1. Repair built-in apps such as the Search bar, Start menu, and Settings:
Open Powershell with Admin or CMD with Admin (Press Windows key + X then click Windows Powershell(Admin))
Copy the line of command to Powershell then press enter:
Get-AppXPackage | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppXManifest.xml"}
Then hit Enter, once the process is done, restart the PC and check.