Can't Type In Search Bar and Windows 10 Built-in Apps.

Clearly those apps need to be closed.

You say

I tried this again but when I get to the part where I have to enter this command into the cmd prompt:

Get-AppXPackage -AllUsers |Where-Object {$_.InstallLocation -like "*SystemApps*"} | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppXManifest.xml"}

a. Could you advise where that command comes from please? (quote a link to a tenforums tutorial for example)?
b. I should be run from Powershell not a command prompt.

It appears to be related to Cortana. Cortana is unrelated to search in 21H1.

It's also not what I suggested you did.

Note:backing up to a cloud service is going to be incredibly slow for most people with any significant amount of data because of upload speed limitations. Most people use local disk store e.g. for disk imaging or other file backup.

Naturally off-site backup is better..

I tried to rebuild the index once again. No effect, the search functions, Cortana, etc are all still broken

Kindly specifically confirm you looked at the count of indexed items as I asked.

Have you perfomed an in-place upgrade repair install yet? You need an iso file for your current build, freely downloadable.

I always wonder what actually leads to these issues, which I've never experienced...