User Agent: Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:92.0) Gecko/20100101 Firefox/92.0

Steps to reproduce:

Using the thunderbird 91.2.0 snap on Ubuntu Hirsute on a xfce session, the preference option to use native notifications is enabled but thunderbird displays its own notification when receiving new emails.

Using the 91.2 deb from impish on the same system has the same issue.

78.13 does correctly use the desktop notifications though

Actual results:

The debug console has an error logged

mail.notification:
Exception { name: "NS_ERROR_FAILURE", message: "Component returned failure code: 0x80004005 (NS_ERROR_FAILURE) [nsIAlertsService.showAlert]", result: 2147500037, filename: "resource:///modules/MailNotificationManager.jsm", lineNumber: 342, columnNumber: 0, data: null, stack: "_showAlert@resource:///modules/MailNotificationManager.jsm:342:23\n_fillAlertInfo@resource:///modules/MailNotificationManager.jsm:205:10\n", location: XPCWrappedNative_NoHelper }
MailNotificationManager.jsm:345:22

Expected results:

Having the new email notifcation displayed using the native system from the desktop (notify-osd in the current session)

Is it the same if you download a tarball directly from https://www.thunderbird.net? I tested with an xubuntu-21.04 live image just now, it worked for me. You can run this script in DevTools to quickly show a native notification

alertsService = Cc["@mozilla.org/system-alerts-service;1"].getService(Ci.nsIAlertsService);
alert = Cc["@mozilla.org/alert-notification;1"].createInstance(Ci.nsIAlertNotification);
alert.init(null, null, 'test title')
alertsService.showAlert(alert, null)

It's the same with the tarball. Interesting but your script from the debug console does properly trigger a notification from the desktop system and not from thunderbird but new emails still do display a thunderbird custom one. Does the NS_ERROR_FAILURE give any clue perhaps?

Does this still reproduce for you when using version 102, via Help > About ?

Yes it's still an issue using 102.3