I dont know this may help you or not but I think give it a shot. Go to Gmail from your PC's web browser then in Settings and further in Labs tab and search for Unread message icon then click Enable.
This will show you unread icons on web browser's tab. Try this which might solve your issue.
Related question: the Tesla Gmail and text badges work fine, but my phone badge keeps telling me I have a phone call when I don't. I've tried turning off the phone badge for a few days, but as soon as I activate it again, the badge says I have one missed phone call or voicemail (not sure which it's reporting.)