All of this x 2. Masturbating is part of a healthy sex life but not when it's at the expense of others.
There shouldn't be awkwardness about it.
Why had he turned down more sex in favour of his right hand? It's downright weird. And yes, occasionally, it's easier and sometimes less hassle to have a self quickie, but it sounds like his masturbation is very habitual. Habits can be hard to break away from, and he doesn't sound like he wants that to change.
You can leave if you choose to. It's easier to do it sooner rather than later before your life becomes more enmeshed.
He may appear to be loving, caring, and respectful. But what he's doing shows a distinct lack of respect for you and your well-being. Interrupted sleep will have a long-term negative impact on you. You've already had to move bed rooms, he has chosen to masturbate over spending the night with you.
If you put up with this, over time, it will eat away at your self-confidence, self-worth, personal boundaries, and self-respect. Is it still worth staying together, knowing that?