Safari 12 - Favicon in Gmail tab shows incorrect e-mail count
Unfortunately, there is no solution for this at the moment.

This is a known bug in Safari 12, and has to do with the way website favicons shown in Safari tabs are cached. My experience so far with Safari 12 in macOS High Sierra and macOS Mojave has been that favicon once cached for a website is not refreshed automatically.


Safari favicons don't support updating


An advisable approach here would be to file a bug report with Apple. I have already done the same. Having more reports for same issue increases the likelihood of an issue getting resolved.