Getting error message when opening report server home page ( found 163 but 162 needed)
Talked through with the Asker in chat but in essence:

Database Engine (SP3) and Reporting Services (RTM) are now installed on the same server but experiencing incompatibility since the "naïve" Reporting Services (installed from a RTM media - overwriting the now-uninstalled updated version) is seeing a more recent (updated) Database Engine ReportServerDB version than it can handle. Database Engine has been upgraded since the original install (via Windows Update or whatever applies to that environment) to SP3 but RS has now been reset to "naïve" RTM version.

Update the installed Reporting Services with SP3 and any CUs to match the installed Database Engine version, restart and re-try. There may be some downtime for users depending on whether it requires a restart so advise/schedule that accordingly.