This feature first sends the encrypted username to the password checking service and matches it with the compromised username with the same username, which is not shared with anyone including Google.
However, it is still an extension so far, not only can detect leaked passwords, but also seems to work well when judging weak passwords or leaking passwords. When a user logs into a website or service (such as email, social network, etc.), the password checker automatically checks the security of the password. However, the Chrome browser for Android does not support the current extensions. This means the tool can't be installed on your mobile device.
All of this will change in the near future as Google plans to add this tool as the default feature of the Chrome browser. This feature is likely to become a feature common to all platforms. The 9to5Google site has found some new code in Chromium Bug Tracker, indicating that Google is working hard to implement this change.
If users don't want Google to check their passwords, they can also disable password checking on their browser. Depending on the development progress, this feature should be done in Chrome version 78, which Google should release later this year, but users of the Canary and Developer versions should see it earlier.