I reinstalled the app to see if I was misremembering it. The app requests for always on location information upon installation and pairing with the headphones. The garden path in the UX of the app is to allow location access. If the user chooses to not allow location access by tapping the tiny "Later" button, the main screen prominently features a Switch control (which is off) for Adaptive Sound Control, tempting the user to toggle it on, which requests always on location access. Given all of this, it's very difficult to interpret this "feature" in a favorable light.
Fortunately, the app's privacy policy[1] does not seem to mention anything about them collecting location information (but they do claim to collect "country or region"). On the other hand, the manual for the app[2] also has no mention of it requesting always on location access either, which doesn't inspire much confidence. Not to mention the 27 month data retention policy and the policy of sharing with their "affiliates".
After having read the privacy policy, I'm glad I chose not to use the app and will continue to do so.
[1]: https://musiccenter-cdn.meta.ndmdhs.com/headphones/pp/201903... [2]: https://helpguide.sony.net/mdr/hpc/v1/en/index.html