From the database’s point of view, there’s no difference between hitting the database from different points and multiple connections from one prisma pool. All connections are treated the same.
You should be more concerned about how your applications function as horizontal scaling requires different thinking to vertical scaling.
When running multiple servers/instances of your application there’s different considerations, for example session management should always store information with a source of truth (this could be postgres, redis, etc) and not store information only locally otherwise requests that come into server B won’t work because only server A knows that the session exists.
I am also wondering if it is possible to attach same postgres DATABASE, not creating a separate database, to two or more applications (meaning that DATABASE_URL connections string will be same, username, password, database_name etc.)?