Affected the latest Apple Watches too
The green screen issue affects Apple Watch Series 8 and older models. It is less common on Apple Watch SE and Apple Watch Ultra models. Users say that the screen changes color when viewing notifications, when accessing Control Center, on the password screen. While some users reported that the issue was resolved after restarting the watch, some users did not.
Apple has had a similar problem with iPhone users in the past due to software. If this is really a software issue, Apple will fix it with an upcoming watchOS update. The watchOS 9.6 beta version has been released, but it is not yet clear whether it has resolved the tint issue.