JR East Pass Nagano, Niigata area

Please clarify the following:
JR East Pass Nagano, Niigata area does include Toyama.
You can access Tateyama-Kurobe Alpine Route from either Shinano-Omachi or Nagano.
The Tateyama Kurobe Option Ticket can be used from JR Nagano/Shinano-Omachi Station to Dentetsu-Toyama Station on the Toyama Chiho Railway, or from Dentetsu-Toyama Station to JR Shinano-Omachi Station/Nagano Station. (Not valid for round-trip travel or partial trip round-trip travel).
I will depart from Shinjuku JR Station to Nagano Station and book separately the bus to Omanchi Station.
Does the Pass include the return from Toyama Station to Shinjuku JR Station?
If no how can I return without paying additional charges?

As per you earlier answered question. Toyama is not covered.

And with the JR East passes, there is no way to get to or from Toyama for free. You need to use a different pass or just pay for the section outside the validity zone of the pass.

Will any other pass besides JR Pass work?

Hokuriku Arch Pass maybe. It's unclear what exactly you plan to do.

I want to buy a pass to get/from Tateyama Alpine Kurobe Route in addition to buying the add on option.

Then yes you can do that with the Hokuriku Arch Pass as well as with the nationwide JR Pass.