I have an unlisted extension published through the Chrome web store which is already being used. I have a new version which I would like to release just to testers initially, before a full roll out to everyone. Can this be done?
The same thing has been asked here but it was almost 9 years ago, and the answers disagree on whether it's possible or not: How to publish new version of Chrome Extension only to testers
The short answer is "No, it can't be done for a published extension".
According to Chrome Web Store visibility descriptions, you must unpublish an extension before it can be published to trusted testers. Users who already have it installed will get updated to the new version.
In your case, you have to create a new extension with the new code, and a different name like "MyApp Beta" and publish it privately to the list of trusted testers.