A software vendor is claiming that the version of SQL Server that was installed was not SQL Server Standard because the vendor executes a select query for version "select @@version" and the resulting display string shows "RTM"
Ah I can understand your frustration, fortunately you are absolutely correct and the other person is totally wrong. RTM means "release to manufacture" and has nothing to do with edition of SQl Server which is primarily enterprise, standard etc. The SQL Server released first time is called RC ( Release Candidate) which is beta version released for testing and should not be used in production. When officially it is released first time for production its is RTM version. So both Standard and enterprise can be RTM version.
If you see this official doc for Exchange Server
In the following sections, RTM stands for release to manufacturing (the first version of the product).
In other SQL Server 2019 Release note it is written
The RTM build number for SQL Server 2019 is 15.0.2000.5.
It does not says standard or Enterprise.
Does that suffice ?