Hi and Welcome!
Crate training and independence are two different things really... if you want to crate train... you need to teach the puppy that the crate is a GREAT place... put treats in the crate and let the puppy go in but dont shut the door... after a few times, shut the door for a couple of seconds and then reopen and give a treat... keep doing this until you are building longer and longer periods where the puppy is in there. I think training a puppy that a crate is a good place is a good thing because there are times they may be crated (at the vet, at a groomer, etc.)
But independence is a different story... a lot of it is personality I feel like.. .I treat mine exactly the same and one is very independent and one is not. But try giving your puppy toys they can play with alone like Kongs, Bully Sticks, or other chews. Say you spend a lot of your time in the living room of your house, put a bed and a fun toy in your bedroom, so that he sees that even if your not in a room other fun things are.
Let me know if any of that did not make sense,
I am sure others will have good recommendations as well!
Good Luck