MailSignal is an app that displays a floating window over other applications with a list of your mailboxes and the number of new emails in Gmail and Outlook. Up to two accounts are free.
For work I need to use Microsoft Outlook, while for personal mail I use Google. At the same time, I want to see how many new emails arrive in both inboxes without having to open them.
This can be solved with MailSignal, which adds a floating window above all other windows showing your mailboxes and the number of new messages in each of them.

The app doesn’t have many settings. You can add Gmail, Microsoft 365, and Microsoft Shared Mailbox accounts, as well as choose where a mailbox should open when you click on it.
Pricing
You don’t need a license if you only use two accounts. Otherwise, the app costs $25.