One option is you can run a separate OH 2.5 instance to run this binding. Then use the Remote openHAB binding in OH 3 which will let you mirror the OH 2.5 Items in your OH 3 instance.
Sure. How do you represent all this in your Items? That will drive the approach for the rule.
However, I might offer a different approach. You can make your code that builds the request as a library function(s) (see OH 3 Examples: Writing and using JavaScript Libraries in MainUI created Rules). Then you can make multiple rules that call this one function with the right arguments. That might be easier to write and understand and still avoid duplicating lots of code.
Another approach might be to set this all up in the HTTP binding and use transformations. Then you might not even need Rules at all. From what you’ve described I’m not convinced you even need Rules for this. At most you might need a JavaScript transformation. Then you can model your TV using separate Items (which is more OH appropriate).
The Member of trigger is still supported by all openHAB rules langauges.