So the meeting was not sent to your calender, but to a calender in a Teams channel (shared mailbox).
If the meeting was sent to your calender in Exchange/Teams (and notification is on), you will get notification for receiving the message in Outlook App/Web.
If the meeting invite is sent to a shared calender there will not be any notification popups shown.
However, if the meeting is created in the Teams channel (so not only invite, but the meeting is actually created in a Teams channel from Teams) you will get a Teams notification when the meeting starts.
So this is more a problem of using the features correctly than getting notifications from a shared mailbox.
Your question was: Is there anyway you can get notified and indeed there is. Using Power Automate (Flow) you can send yourself a chat in Teams when a new meeting is created in the shared mailbox, that's not that difficult and you can use this template: "Send a push notification when a new email arrives in shared mailbox" as a start.
/Kenneth ML