Pregnancy is not per se a disability and lots of women at 32 weeks are still going to the gym. I’ve even seen a few run 5-10k on a treadmill!
I do think it depends a bit on who the sitter is. If it is a fit young person, then they always should. But middle aged or older and maybe been on their feet all day, does pregnancy tiredness trump this?
It is nice if people are well mannered and offer, but I don’t thing pregnancy alone is a disability right up until the end of the third trimester (twins excepted). I, at nearly 60, would always give my seat up to anyone who looked like they were struggling or very heavily pregnant, but I wouldn’t necessarily to someone young who looked perfectly healthy and middling pregnant.
As for ‘baby on board’ badges, I think they are quite passive aggressive. And, as to asking, it depends how you do it. If you say ‘I’m really sorry, I need to sit, I am not feeling great’, I would always stand. But if someone just pointed to a badge, I would be tempted to say that they were pregnant, not sick.