Solutions to RLS (Row Level Security) in PostgreSQL for Desktop Application?
I believe you're problem is similar to one I've faced a few years ago, while trying to design a multi-tenant web application with a single underlying database schema.
There's an interesting article by AWS that can point you in the right direction.
The core of it is:
CREATE POLICY tenant_isolation_policy ON tenant
USING (tenant_id::TEXT = current_user);

There are several different approaches, but the one I ended following is this:

Use a different database user for each connection coming from your desktop PCs. This should match your RLGroupId, if I understood correctly.
Apply a Policy to every table where data segregation by RLGroupId should be enforced

Hope this helps.