to grant RDP access right to Database Server.
RDP is a Windows feature and has nothing to do with SQL Server.
We prefer to give me db_owner to the those databases
Jobs are not really related to single databases, dbo permissions won't work.
he argues that checking SQL Agent Jobs need sysadmin right.
Absolutly not, see https://learn.microsoft.com/en-us/sql/ssms/agent/configure-a-user-to-create-and-manage-sql-server-agent-jobs?view=sql-server-ver16
There is a request by consultant
By that request I would say he is not the best in his job; but that's only my private opinion.