Backyard, kennel or crate for my puppy after 4 months?

If the current crating regimen is working well for you (and him), he's not having accidents, he's getting enough exercise and his crate is large enough to accommodate him, I think you're fine to keep doing what you're doing. 4 months is still fairly young. You can gradually introduce him to more freedom in the house a little at a time, so that one day when he's mature, he doesn't go right from the crate to full independence.