Sorry, forgot to mention. I have an optical cord running from my TV to my audio receiver which is a Sony DTR ST897 (old receiver). The wireless headphones, RCA WHP141, are plugged into the Sony receiver thru the quarter-inch headphone jack using an adapter.
And for the other folks suggesting an adio extension cord, I feel like the static would still be there even using an audio extension cord. So that’s why I’m leaning towards a corded headphone now.
https://www.amazon.com/dp/B0778V7RVR/ref=vp_d_ac_pd
Your RCAs are 900 Mhz. The Bluetooth should work fine and work at 2.4 Ghz.
A headphone extension cord will not introduce static. I am using a 100' extension cord to get music from my house to my barn and there is no static whatsoever.
Buy your new corded headphones, and use the extension cord with them. I have an extension cord that has a inline volume control that is helpful.
Have you tried cleaning the jack/adapter for the older receiver? A little corrosion can cause physical contact problems.