No, in order to show to the world what is going on up there you only need a video stream. The networks on earth can retransmit that to they viewers if they wish.
How do you think video from the ISS gets shown on NASA TV? They aren't operating a TV station on the ISS; they are sending a video stream to NASA most likely using TCP/IP. I assume the same thing will happen with video coming from the moon.
I get that you are chomping at the bit for an opportunity to DX the moon but the hard reality is that it makes no financial sense for anyone to put a TV station up there. It doesn't make sense now, and it won't make sense on the moon until there are a significant number of people up there. And since the moon has no oxygen, it will make sense for all the colonists (or at least all those sent by a single entity) to be confined to a pretty small area, which means that they will likely all have wired or wireless Internet access. So why do they need a TV station? They don't with today's technology, and 8 to 15 years from now (to use your timeframe) there will be an even less compelling case.
In fact there is a part of me that wonders if the switch to ATSC3 is the beginning of the end for terrestrial broadcasting. A lot of people see no need for it and won't go out and buy new equipment to receive it. In the meantime, IMHO anyway, most of the recently-made shows have been of poorer quality than the older shows, except for the fact that the older shows were in standard definition and the new ones are in HD. I find watching regular television is a less enjoyable experience with each passing year - there are still a few good shows but with most of the newer ones I can't stay awake long enough to finish an episode. I suppose that is partly due to my age but I still can't shake the feeling that the broadcasters have put their golden goose in the oven and they keep raising the temperature (the cost to viewers) and one day will find that the younger folks just aren't that interested in the crap they are producing (already many young people would rather play video games or watch TikTok videos than watch TV). So I would not even guarantee that in 15 years TV stations will still be a big thing on planet Earth, let alone on the moon.
And if I am wrong and TV continues to be a thing, I would bet that you'll see a TV station on Mars before you'll sever see one on the moon, partly because a TV station on Mars would not have nearly as much potential to interfere with signals on Earth.