Only you know your DC, OP, but IME with my own autistic DC of similar age, I find the more rigid the boundaries, the more they push against them (you seem to allude to similar with the suggesting hobbies comment).
So I would be doing the same as you and letting them gently explore things too, but I absolutely relate to your anxiety about what the future might hold for them and whether I should be taking a firmer stance as a parent, not least as they'll be in a brand new environment that could mean things go either way depending on who they meet and which social circles they fall in with.
As PPs have said, the key is keeping the lines of communication open with them. I think I'd want to reassure them that they are the same person to you regardless of how they identify, as there are a number of detransitioners nowadays who feel stuck as their parents have made such loud noise about celebrating their transness that they feel they're stuck in that image they've created for themselves now with no route back.
I think just treat it similar to a goth phase or anything else - experimentation with clothes, makeup, names, identity, etc is totally normal at that age and is a part of growing up, so as long as they aren't planning an making any rash irreversible decisions, then I would just go with the flow and focus on the other aspects of starting university and what will be an exciting new chapter for them in loads of other, non-gender-related ways too.
There's only so much control you can have over the situation at this point, so don't be too hard on yourself - you're doing a great job of being a supportive parent in an extremely challenging environment, so just go with your instincts and remember that you know your child and how to support them best.
Your partner sounds like an overbearing arse. It's absolutely none of his business how you parent your child, and the fact he's being so vocal about your parenting decisions would have me running for the hills from that relationship. As a first step, I would stop confiding in him on the issue, as you know he's not going to be supportive of you making your own decisions about your relationship with your own child, so no good can come of discussing it with him.
I wonder if you'd be quite as stressed out by this whole situation if you didn't also have him criticising you and suggesting you're doing a crap job as a parent. You and DC are at a point where the pressure really needs to be eased, yet your partner seems to be vying for the opposite.