Zulip is designed to use your OS/browser's timezone for this and all other displays of times (say, when messages were sent). This is usually what you want, since it means you just need to make sure your computer's clock is correct and not manually update every app you're using.

In the issue you linked, the root problem is that the anti-fingerprinting browser feature has the browser pretending that its preferred timezone is UTC, resulting in the user seeing all times displayed to them in UTC.

It has nothing to do with the "global times" feature -- that feature just renders an element in your message in the same timezone that it renders the timestamps.