1C

Should Vera have realised it was a body sooner?

Not necessarily. From the position that the woman was described as sitting in it could have been someone asleep or just with their eyes closed. Vera was in a hurry to get changed and out of there so she didn't speak to her.

I don't hang around many steam rooms but I've been in them before. It seems if someone else is there they usually nod or say hello. If someone was there with their eyes closed I don't think I would realize immediately that they were dead.

As I said before, it was kind of foggy in there and the lady could have been sleeping so under those circumstances we can forgive Vera for not being more observant.

Vera was too worried about her own body image and wanting to be out of there as quickly as possible so we can understand her missing it, until she realised the person was too still.

I don't see how she would have spotted it any sooner. In fact, I think it was only due to the nature of her job that she recognised the stillness of the body for what it was.
Mind you, I realised before Vera did that this was going to be a corpse... ! : )

As I said before, I enjoy steam rooms and I have been in some where I can barely see my hand in front of my face let alone someone else sitting in the room. I thought the beginning very plausible.