

I’ve never heard of a gender/sex distinction between ‘woman’ and ‘female’, what are you basing this on? By whom is this distinction ‘supposed’ (as you put it) to be a thing.
I doubt the general public would agree, anyway. In the Cambridge Dictionary, I find ‘female’ defined as ‘belonging or relating to women or girls’
You may think your definition of ‘female’ should be the correct one, but it’s not the common one at the moment. I would think it’s strange, though, if you couldn’t refer to a trans woman as ‘female’, which your distinction seems to imply.
If you’re purely referring to ‘female’ as a noun, I do have a similar intuition about ‘female’ (noun) vs. ‘woman’, but it has little to do with objectification and more to do with ‘female’ generally being used in a biological sense, specifically non-human animals.
As an adjective, ‘female’ is pretty neutral, though.