How thick should plywood be for hardwood flooring?

In the process of removing the 1/2" particle board and carpet in a loft so hardwood flooring can be installed (I'm not installing the hardwood, I'm having a professional do it. I'm just removing the particle board and doing the grunt work.) There's a 1.5" tongue and groove cedar subfloor that runs perpendicular over the joists/beams, and this subfloor is also the exposed ceiling for the bedroom and kitchen that are underneath the loft.

Just for my own curiosity and education, what thickness does the plywood underlayment that goes over the subfloor need to be? Should it be tongue and groove plywood or something else used for an underlayment under hardwood flooring for my situation? Particle board seems useless since it just crumbles and disintegrates, swells if it gets wet and offers no structural integrity, rigidity, etc., and plywood is lighter in weight that particle board.

Also, would it make sense to go through the subfloor and reinforce the subfloor to the joists with screws to secure the subfloor to reduce any squeaking and loose boards before the plywood underlayment goes down?

Thanks!

Here's a cross-section of the 1.5" cedar tongue and groove subfloor:



Here's a few pictures of the subfloor/ceiling after the particle board has been removed:







Here's a picture of the ceiling of the bedroom that's underneath the loft:

I’m gonna say 1/2” to 3/4”. You can’t go wrong with 3/4” but do you really need it. The 1.5” subfloor should be plenty enough to limit deflection. You just need the plywood to smooth things out. The 2x is your subfloor, the plywood will be underlayment. You don’t need T&G for underlayment. I would definitely go around and refasten any loose or squeaky boards to the joists before you install the underlayment.

I cannot answer the question. But I do love the look of the floor in the balcony, and the ceiling that shows below is beautiful.