MY first question is what is below this deck and why on the second floor . Maybe post a pic of the house side where this is going to help too. I do not usually like decks that are raised to have anything but a flooring that will not drain water to what is below it so I need context. Post the additional info and pics here in comments

Here is the picture. My house is built into a hill and from the back the main level is the second level. I have a walkout basement

So the flooring on that deck will all need to be waterproof and that will require something like Duradek to keep the underdeck dry . Who designed this ? That is who should be doing the waterproofing since covering it will not really keep the rain out hence it will wet the lower area too .

Nashville is hot and highly HUMID, and nearly as humid as Florida in the summer. . Probably well over half of all weather in the USA comes from the west. ......

I would do a composite, Trex or similar. Don't forget termites: )

We have the same set up. Our screened porch covers our open sided outdoor kitchen below, so it needed to be waterproof. We went with a porcelain tile and pedestal system from The Tile Store. Beneath the non grouted large format tiles, there is a waterproof lower floor that slopes away from the house to the edge. I believe there is a 4” drop, letting the rainwater flow between the tile edges, down to the sloping floor, and out a slot on the facing of the edge. The kitchen below has a regular looking ceiling just below the sloped rubberized inner ceiling. I’ve probably made a mess of an explanation, but it works!

Sorry. I tried to add pics of the kitchen below as well, but Houzz is being its usual cranky self about adding new photos. The pedestals build on each other at the corners of each tile the closer the tiles get to the screened edge, keeping the porch floor level, and raising them from the sloped floor below.

Instead of screening in the porch, why not have single pane glass enclose the room, then you won't have to worry about rain (when it does ran and you could go with deck boards.

It would make it a more usable room, and you could have sliding patio doors with screens for when you want to open them up.

Investigate out door shutters which will keep the deck dry, and while doing that, also protect the indoor room behind the porch.

https://eliteshuttersnc.com/porch-shutters-shades/

Our porch floor is painted wood.

The screens do a better job of keeping the rain out than you might expect. I don't think I've ever seen water pool on the floor, even after truly nasty storms.