reinstall

From a Time Machine backup—Restore

Restore items backed up with Time Machine on Mac - Apple Support

https://support.apple.com/guide/mac-help/restore-files-mh11422/mac

or

From Recovery reinstall the macOS on top of your existing macOS.

Recovery: https://support.apple.com/en-us/HT204904

There is no stand alone Messages.app to install independent of the macOS.

You couldn't have as it is protected by the system:

Look in the Applications or Applications/Utilities folder.