How can I start an RDM new session by clicking on an RDP uri example rdp://serverip

I think that you manually have to setup a protocol handler:

https://docs.microsoft.com/en-us/windows/desktop/search/-search-3x-wds-ph-install-registration
https://docs.microsoft.com/en-us/windows/desktop/search/-search-3x-wds-extidx-prot-implementing

Regards

I have set that up, but what is the call to relay to RDM to have RDM start a connection based on the parsed information?

Here is the help link for the command line parameters

https://help.remotedesktopmanager.com/index.html?installation_commandlinearguments.htm

Regards