Do Sony headphones store data, or is it just the app?

I'd like to get Sony WH-1000XM5's, but the app collects a lot of data, and has a lengthy EULA with a hidden privacy policy (the link to it is to a Japanese page). If the headphones don't store the data and are only able to collect the data when connected to the app, I can just use an old phone to connect to the headphones and not connect the headphones to that phone most of the time. If they do …

app collect data don eula headphones hidden japanese link policy privacy privacy policy sony store