Maybe you can convince her mom to start programming. That would add another role model who was doing it.
I think that programming will be something that mainly AIs do in 8-10 years. It's certainly important for her to learn problem solving skills and understand technology but maybe not actually important to be a programmer.
But for it to stick or not be a waste of time, you may need to allow her to find her own way.
So maybe consider opening up that non-TV time to allow for her to choose her own constructive activity. You can require her to choose something that uses technology to do some type of problem solving or otherwise constrain it. But try to be open to her own exploration. If she is doing something just to satisfy your rules then she is likely to abandon it when you stop making her.
I think also that you are fighting the natural subconscious tendency of humans to copy what other people (especially role models) are doing, and programming is already relatively unpopular among women. Which makes it even less likely that she will stick with it without your pushing her.
And now in the next several years programming will also not be so popular among men, as new versions of GPT etc. come out year in and year out with better and faster reasoning, discouraging students from trying to compete with AI.