I should add, sad because it is very hard to build and plan a life where you do not know where you will be in 3 or 6 years. For example, why would you try to buy a house if you don't know what will happen? Because of all this I am probably considering to not even bother with H1B.

The GC application should follow the H1B immediately. Don't accept an offer from an employer that cannot promise you that they will do that. Either they don't know what they are doing or they can't imagine you still working there several years later.