ProtonMail (unofficial) by Gitladen7

Unofficial ProtonMail extension. Provides notifications and makes it possible to close the ProtonMail tab, and even the browser, without getting logged out.

Issues and help: https://github.com/gitladen7/protonmail-webextension/wiki
Source code: https://github.com/gitladen7/protonmail-webextension

General Settings:

• Fetch interval: Select how often the extension will check for new emails.

Settings:

• Persist session: Check it to keep the sessions in browser memory.
• Persist session even if browser is closed: Check it to save the sessions to disk. WARNING: Your mailbox password will be written to your hard drive.
• Show unread count badge: A badge will show on the extension icon with the number of unread emails on the INBOX.
• Show notifications on new emails: If checked then the extension will show a notification when you receive an email.
• Enable peeking: If checked then you will be able to see a list of your inbox unread emails in the extension itself.

FAQ

Which are those "2 other sites" on the permissions?
Those sites are app.protonmail.ch and protonirockerxow.onion, both of them official ProtonMail domains.