@Sebastian: Thanks for the suggestion. I tried to run the SQL file from Host > SQL. Unfortunately, I'm still stuck with the following error message.

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System.Data.SqlClient.SqlException (0x80131904): The ALTER TABLE statement conflicted with the FOREIGN KEY constraint "FK_PortalSettings_Portals". The conflict occurred in database "xxxdb", table "dbo.Portals", column 'PortalID'.
at System.Data.SqlClient.SqlConnection. (SqlException exception, Boolean breakConnection, Action`1 wrapCloseInAction)
at System.Data.SqlClient.SqlInternalConnection. (SqlException exception, Boolean breakConnection, Action`1 wrapCloseInAction)
at System.Data.SqlClient.TdsParser.ThrowExceptionAndWarning(TdsParserStateObject stateObj, Boolean callerHasConnectionLock, Boolean asyncClose)
at System.Data.SqlClient.TdsParser.TryRun(RunBehavior runBehavior, SqlCommand cmdHandler, SqlDataReader dataStream, BulkCopySimpleResultSet bulkCopyHandler, TdsParserStateObject stateObj, Boolean& dataReady)
at System.Data.SqlClient.SqlCommand.RunExecuteNonQueryTds(String methodName, Boolean async, Int32 timeout, Boolean asyncWrite)
at System.Data.SqlClient.SqlCommand.InternalExecuteNonQuery(TaskCompletionSource`1 completion, String methodName, Boolean sendToPipe, Int32 timeout, Boolean asyncWrite)
at System.Data.SqlClient.SqlCommand.ExecuteNonQuery()
at DotNetNuke.Data.SqlDataProvider.ExecuteScriptInternal(String connectionString, String script)
ClientConnectionId:4a3d938c-52d0-4499-bf60-8985c4b9029f

-- add back foreign key
ALTER TABLE dbo.PortalSettings
ADD CONSTRAINT FK_PortalSettings_Portals FOREIGN KEY ( PortalID ) REFERENCES dbo.Portals ( PortalID ) ON UPDATE NO ACTION ON DELETE CASCADE
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@Sebastian: Thanks for your help.

I don't think it is related to database user privileges as the upgrade was almost completed on the site. Any other inputs here?