It doesn't matter that he's 26 and a grown man. This is his childhood home. Some woman moved in, he had to accept her, then she had a baby and he isn't welcome anymore. When it comes to our parents, we react on an instinctive level, and he will feel hurt and rejected if this handled badly. I think it makes a difference that the age gap is between him and a half-sibling - I think it will add to the possible feelings of rejection/being replaced.
He should always be able to stay with his dad. Whether he should always have that room is a different question. In time, when this is all properly dealt with, being able to stay with his dad when he needs to is likely to take the form of sleeping on the sofa or sofa bed in the living room. He's family. He doesn't need to stand on ceremony, he just needs to know he will always be a part of the family, no matter how squashed or imperfect things are. With family, you suck things up.
In the short term, it sounds like you'll have to use the living room for someone if you really can't keep DS in with you anymore. You could put the toddler there, but as the toddler will have very different sleeping patterns to everyone, that will take away your communal space - for all three grown-ups.
I wonder if you could frame it to DSS that putting the toddler in his room would be less disruptive to his sleep/daily activities and while he is welcome to stay with you as long as he likes, sleeping in the living room might help get him moved up the housing list as he technically wouldn't have a room?
I'd ask DP if he thinks it would be better having the conversation with you or without you and let him lead it. The ultimate aim is for DSS to want to move out as soon as possible without feeling like he was pushed. You're not wrong in wanting the room back for your DS, but you just have to approach it sensitively.