You can check if you have a Push permission for suspect domain(s) like shown at the bottom of the message and revoke this permission. See "How do I revoke Web Push permissions for a specific site?":

• https://support.mozilla.org/en-US/kb/push-notifications-firefox

All I could read was "CAD 3.8.2" and "Cookies were deleted". The rest disappeared too fast to read. This appeared after I closed a tab to a site I had signed in on. It didn't appear after I just visited a site without signing in.

The Cookie AutoDelete extension is doing that. Go into the CAD Settings and either disable Automatic Cleaning or set it to delay something like 30 seconds before doing the cleaning.

There is also an option further down the page to enable/disable Show Notification After Automatic Cleanup if you just don't want to show the notification at all.