My 1985 Mazda Rx7 will start but when I let my foot off the gas it will stall.

I havent seen one with the hood open since 1984. But the thing that jumps out at me about your runability is, opening the throttle adds air. and having it cough when you open the throttle indicates lean. This seems you are in the area that testing should reveal something. Back fire can indicate fuel in the exhaust .and igniting it? Since the car is around thirty years old, and specialists have bought them all up, there has not been much of them in the mainstream. You need the tests, and the shop equipment, report your results. A regulator can be manipulated during the test to change readings and see that it can work, is working and see the fuel pump's max output. Injectors that are malfunctioning can be tested by sampling as well as electronically. I hope discussing these factors can get someone with current experience with that model to write in, and share their experience.

Possibly faulty throttle position sensor or dirty/faulty idle air control valve or dirty throttle plate.

Does a rotary have an idle air control valve ? Or a throttle air bypass ? Or does it just have a drilled butterfly valve in the throttle body, it has been eons for me.

I show the parts available for this model.

Just my thought,s to your question,if back fire,was random,and now run,s power less as you say.if you have not, already checked it,im thinking timing issue,

You are aware that it has a wankel

I read a little tonite about the backfire, the fluff in the exhaust after letting off can be more unburned fuel than usual. Spark plugs do not last long. And when timing is optimum, they produce a coloration at the bend in the plug's ground electrode. But you own a rotary, you must drive around with a plug wrench,plugs, and a quart of oil in the passenger seat, right ? You can read the same discussions by googling causes of rotary engine backfire. I am not convinced of any timing related concern unless your first new plug check does not produce the coloration at the bend in the ground electrode of your plug.