When opening the developer tools, Omnibug does not appear in the list of tabs.
Unfortunately this is a new bug within Chrome itself that has appeared in v82 for all extensions that use the developer tools window. We've opened a ticket with the Chromium team in early June when the problem first appeared but there has been no movement from the Chromium team on this lately (mid July 2020).
This bug seems to happen most when navigating to a page. Usually you can get around this by closing the developer tools and re-opening it once the page has loaded. You can follow us on Twitter for the latest updates.