Do Sims recognize what counts as a Kitchen/Bathroom/Bedroom for renovations?

Yes, Sims recognize specific room types. If the job is for a bathroom renovation, make sure you only renovate the bathroom. Changing the wrong room, even if it looks great, will lead to no payment and a drop in reputation. Stick to the assigned room and check that it’s labeled correctly in Build Mode. And you're right the career is pretty buggy, so it's not just you.