I think you are right actually.
I have a friend who currently shares a bed with her 13 year old (friend's marriage is struggling) and I think that's somewhat unhealthy and have (politely and respectfully) told my friend so. (We are close enough friends to share frank opinions like that).
In my view, teens and tweens need their own private space for things like private phone calls, trying on clothes and make-up..... And, sorry to name what seems to be the elephant in the room - masturbation! I think it's vital for teens and tweens to be able to explore their bodies and their sexuality like this IF they choose to.
I think mom probably does need to set the living area up into a sleep space for her when daughter is there. At one point when I was looking for flats for DD and I, and struggling to find an affordable two bed in a decent area, I was looking a Maisonettes and considered this.....
But I prioritised finding a two bed for the reasons stated above, and even though the flat wasn't ideal in other ways (kitchen is part of the living room; no outdoor space,) - it really was my main non-negotiable.
I DO think that if at all possible your step daughter's mom ought to be looking for more suitable accommodation. (And I realise I don't know their finances or house prices in your area, etc - what I am suggesting may be impossible). And I am not prude - I will get changed in front of my daughter, talk to her openly about most issues etc..... But I wouldn't expect her to share a bed with me on the regular.
I don't think there is anything you can do, but could SD's dad have a word? Is their relationship good enough?
If I hadn't been able to afford a place to live with separate rooms for DD and I, I would have considered asking her dad for financial help with the situation. Would your husband be willing and able to help his ex and his daughter in this way?