Do I approve of sex work?
So, yes, sorta, mostly, but I don't think it's straight forward.
For one, sex work is a very broad category that ranges from selling feet pics to having sex to which you wouldn't otherwise consent with strangers. So under that large umbrella of "jobs wherein you assist someone with getting their rocks off in exchange for money" there's a lot of variation and differing considerations for the impacts on the workers and the clients.
So I guess I approve of sex work in the general sense that I approve of any service industry labor that doesn't intrinsically harm the worker or the consumer. But on the other hand, sex work, particularly having sex, and even stuff short of having sex, bares some higher risk than your average behind-the-counter job. There's risks of violence, disease, and emotional or psychological harm, some of which is higher because of illegality or stigma, but some of which is higher simply because of the intrinsically intimate nature of sex. And sure, there is something kinda squicky about commodifying human intimacy.
But on the other hand, the demand is there (not like I don't consume porn), so the supply will always follow to meet it. So best you can do is ensure that whatever labor sex workers do is as safe as possible, and that the people who do the labor do so freely (to the degree possible in a society that's still capitalist).