Gmail Chrome shortcut + unread message count in Windows 10 taskbar or unread count in system tray

Option A: activate notifications for gmail and they will show up in windows in the bottom right corner and show a notification count. Make sure that all options are set in windows notification center.

Option B: use gmail as Progressive Web App (PWA). Just go in chrome in top right corner option on "More tools" and "Create Shortcut" and check open in new window. Now you can add Gmail as a dedicated shorcut in taskbar. Combine that with option D and even option E and it will look like this.

Option D: Why not change the taskbar settings to always show labels, instead of just a single shorcut.

Option E: use TabModifier to change the title and the favicon of tabs, based on custom rules.

Option F: Use Vivaldi, which includes a dedicated feature for tab notifications. Since it's chromium-based you can keep your chrome extensions.

There are many more ways to get notification on your windows desktop, which is why I don't recommend a custom hack to change the shorcut icon in the taskbar. Would it be worth the effort if the result would be the same?