Weird that 2 more people post, just to ask the same thing I asked :-)
If you want to limit access to Dataverse, then you need to add a Security Group to the Environment and it will limit access to those added there.
But by default, people have no roles in Dataverse, even if they have a license, so they are restricted from doing anything at all.
But I was able to snag a screenshot before it poofed.
The issue is, a person doesnt just "have access", you must grant it, so I am not sure why you built an App that purposely connectors to another environments Dataverse (using what connector??? since the OOB ones wont do that. are you using the HTTPS connector?)
Anyway I do not really follow what you are asking and why because all you have to do is NOT grand them permission.
As for access to data, never give users access to a single App that connectors to multiple envioronments.
So right now I don't know how or why you have an issue, unless yuou are blanketly giving access to everyone to every environment. That's fine if you are, but you still have to give them access to the data or yes, use a Flow to have another account do the work, as long as the user has a DV license, then thats it.