chrome.google.com/webstore/detail/checker-plus-for-gmail/oeopbcgkkoapgobdbedcemjljbihmemj
Step 1
Disable all notifications.
Step 2
"Button click action" => "Open Gmail in new tab".
Step 3
"Show icon animation" => uncheck.
Step 4
"Show tooltip when hovering over the button icon" => uncheck.