Google Home device's issues with staying connected via Bluetooth isn't a new problem. Users have been complaining about the issue since 2018. But it took Google until this year to publicly acknowledge the issue and say that it is working on the problem. The Google Nest account on Twitter replied to a user reporting the problem. The company said, "We're sorry for the trouble! Our team is already aware of this and we're working on a fix, we'll bubble this up to our team and check back in once we have an update. Hang tight!"
A specialist on the Google Nest support also acknowledged the issue, saying the team is working on a fix. They're encouraging users to send feedback about the problem via voice command by saying, "Hey Google, send feedback," and use the keywords "GHT3 Bluetooth IN keeps on disconnect." Now, we're hoping the company fixes this relatively old problem quickly.
Source: Android Police