My DS1 will be 2 years and 3 months when DS2 arrives.
We do have a 3 bedroom house but it's a town house, so the spare room and the living room are on one floor and then the small bedroom and master bedroom is upstairs. We do want to move eventually but with 2 sets of nursery fees, maternity etc coming our way, we simply cannot afford it quite yet - more likely in 2023. We're in London.
I like the idea of having the downstairs spare room as a play room/ spare bedroom with a sofa in it as this creates an open space for the two of them to rummage around and the older DS1 gets, the more toys we have (I do swap them etc but I can't see it getting much better when number 2 arrives).
After all this backstory, have you had success putting both your children in one room at such a young age? It works with the space, the health visitor advised me to put DS1 in a normal bed once he turns 2 but as long as he's happy in the cot, I will delay the transition slightly x