So we know that Google calendar sent the email notifications directly to
XXXXXXXXXX@hotmail.com, and they were received and sown in your inbox in Outlook until some time ago.
Now something has changed, and there are several possibilities.
- Perhaps Google stopped sending these notifications for some reason: perhaps the address was changed in the calendar settings. Perhaps Google has now some policy not to send these notifications to Hotmail or not to send them anywhere.
- Perhaps Google sends them but Hotmail discards them (does not send them to the user's mailbox).
- Perhaps the messages are received by Hotmail but then instead of being delivered to the inbox are somehow integrated into your Microsoft calendar (that perhaps you have and you don't know about).
- Perhaps they are being sent to to your Inbox, and you check it through Outlook client, and the Outlook client is set to handle them automatically and somehow integrate them into its own calendar (a setting might change by some software update).
Perhaps there are other possibilities. I don't know Google calendar and Outlook well enough to rule out other possibilities or to know how to check what is happening (though I use both, but indirectly. I use the Google calendar mainly through Fastmail's calendar, and I have Outlook at work but I rarely open it. I forward all email. I know that sometimes when people cancel events they are automatically erased from my calendar in Outlook without my intervention. But since I have a copy of all my email also forwarded from work to Fastmail I also get the cancelations as email messages in Fastmail, where I setup the calendar to do nothing automatically).