Presumably people post on here because they want to hear others’ perspectives. I went to EOW visits with my father as a teen after his girlfriend and her 3 kids moved in with him. In my case I was that hated thing, a "NR” “step-kid” with my own room when two of his girlfriends’ sons shared a room. My father had had a previous marriage with a woman who was very cruel to me and awful to him as well (they divorced after 6 mos.) and I can see how he felt “never again!” and took this step in the later relationship to ensure I felt welcome at all times. I’m in my 50s now and of all my dad’s flaws and shortcomings, I still remember and value how emphatic he was in telling me that I was always welcome at his house and had a permanent place.
That being said, for myself personally, I probably would have been OK if I hadn’t had my own room. What counted was the sense that I had a permanent place with my dad and wasn’t a temporary inconvenience to be shoved into the new arrangements. Myself personally, I would probably have felt just as welcome if my dad had made up a comfortable place on the sofa for me before I came, a screen or curtains for privacy, a little of my own space for my own things in dedicated drawers and a clear sense that - when I was visiting - that set-aside area was always mine. With an expectation that I wasn’t an unwanted guest, but welcomed, and everyone treated “my” space with respect in the way I treated his girlfriends’ kids rooms with respect as theirs.
The stepson expressed interest in the new property (as he should - it’s half his father’s, after all). Surely there is some pleasant, not second-rate space that can be made for him, and if not a room, some bathroom drawers and bookshelves/cupboards so he will have some permanent space? Permanent, dedicated space is important, to provide privacy, continuity, indiviuality, security for possessions, AND as a symbol that a person belongs. Unless the OP is trying to purge the new property of his existence, setting aside some smaller, pleasant, welcoming space for him and making an effort to reassure him he is still equally welcome as before, shouildn’t be too difficult?
Kids - even when they get on well with parents - always have more thoughts and fears than they let on. As the move happens, and it’s an obvious downsize, it is a good time to reassure the stepson through behaviour and words that he’s equally welcome and at home as before. Althouhgh you shouldn’t assume he will feel displaced, you shouldn’t assume he won’t. Extra kind words and small gestures cost nothing and may make the difference for keeping his interest in his father’s life high.
In this board, people tend to discount comments that don’t address the tiny precise sliver of question that was asked. But whether the stepson wants to still stay over or not may not have a digital answer, or may change. So the bigger picture matters.
I would also add, coming from a culture that values hospitality, that I feel equally responsible for making anyone who stays at my house feel welcome - whether it’s my relatives or my husband’s. Although that doesn’t mean I do all the work when people stay over, it does mean that I don’t remove myself from the obligation to make people feel at home simply because they aren’t my blood relations.