Disconnect TV from AppleTV and use it's own apps instead. Play whatever music you want through AppleTV.
Better option: disconnect HPs from AppleTV. Then they can play anything while you watch anything else on television. Use the TV's speakers for the TV audio.
Best option: let HPs be used for their intended purpose: good music in rooms/areas generally without speakers. For the TV + AppleTV part of things, buy yourself a Receiver and hook up some great, "dumb" speakers to the Receiver. A good Receiver will easily give you the capabilities to show something on TV while playing something else on the speakers. That's AppleTV HDMI OUT to Receiver HDMI IN... then Receiver HDMI OUT to TV HDMI IN. The "dumb" speakers will connect to Receiver with their own terminals. And you can build out to full surround or ATMOS over time by simply adding more speakers as possible.
HPs were
not designed to be TV speakers. That's something that has been glommed on to the features list. They are likely forever limited to stereo-only audio and they are significantly constrained to only A/V stuff you can connect through HDMI and/or only apps that can run on AppleTV or via Airplay. Pretty much all TV and movies produced in the last 20-30 years has moved
beyond stereo sound. To fully enjoy it as it is intended, you need a
better speaker setup than only stereo.
A Receiver + dumb speakers will basically handle
anything and you can build and enjoy a true surround sound setup, up to true ATMOS. Your ears will forever thank you for going the very best way for home audio. And you can enjoy HPs in their primary use way... and have fantastic & flexible options with a traditional home A/V setup too.
Bonus: good dumb speakers will play and sound as good about 20-30 years from now. Having dependencies on iOS roots, HPs days are already numbered... and Apple will be happy to sell you replacements every few years- even though the speaker portions themselves will likely be in perfectly-good shape. In other words, I see HPs like I now see iMacs. The dumb portion- the speakers or that iMac screen- are hard linked to the tech "smarts" portions. When Apple decides it's over for those smarts, both are "throw baby out with the bathwater" propositions. Dumb speakers having no smarts can't be made obsolete by corporate choices like vintaging nor by software evolutions such as the one that prevented GEN 2 of HP from being able to stereo sync with a GEN 1. Buy great dumb speakers as little as one time and enjoy them for up to the rest of your life... with no audio degradation.
All that said, if I really, really want a 'smart' speaker setup centered around my TV anyway, I go Sonos instead... in which I'll get pretty much all of the Apple-specific benefits of HPs with the much greater flexibility
outside of the walled garden. While I'm not usually a soundbar fan, the combination of
Arc + twin 300s as surround speakers and maybe the Subwoofer module is a great sounding "smart" system... NOT so heavily locked down and/or married to only the Apple ecosystem. If budget is tight, I would start with Arc (premium soundbar) and add the rest in subsequent purchases over time.
That works fine with
Apple Music and pretty much
all other streaming services too,
airplay, etc. You can
command Siri through the iDevice or AppleTV you already have (and will be updating those "smarts" more regularly anyway). And if I already have a couple of HPs, I move them to other rooms without speakers so I can enjoy great sounding music in those rooms.
There is nary a rumor that HPs will ever add surround sound speakers, a center channel or soundbar, or a subwoofer. HPs are probably stereo at best for the foreseeable future. Sonos already has all of that tech worked out, it "just works" and works very well with Apple tech. Want a soundbar or subwoofer or wireless surround speakers TODAY? You can have them TODAY!