Newly added staff not being sent activation email

Peter_KIC Does an admin always have to "approve" when a new staff joins, or does a new staff always have to "accept" the invite to a calendar? Maybe I've misunderstood what you mean, but I've never had this for any of my calendars, so I'm curious.

Since staff were added in the past with no issues, then something must've changed. Just have to figure out what that change was, which involves asking and answering a series of questions.

For the new staff being added, are they new accounts being created? Does IT set them up? Is there any difference from how those accounts were created in the past vs. now, i.e. to their licenses, apps, mailbox, etc.?

You mentioned that existing staff do receive the email if it's re-sent to them, so it doesn't seem like the issue is with the email itself. However, asking just in case:

• For the new staff, have they checked if there are any emails stuck in their quarantine (https://security.microsoft.com/quarantine)? 
• If there is an email filtering system (whether Microsoft or other third party), can you ask IT to check if anything is being blocked for the new staff?

You also mentioned that you're using an existing calendar. If this was a new calendar, it should also be investigated (how it was created then vs. now, etc).

As an existing calendar, you can still ask IT to check if any changes were made to Exchange mailboxes recently. If IT had made any bulk changes to mailboxes, then Bookings calendar could be affected, since they are actually Exchange mailboxes (as can be seen from the PowerShell command for them, which is "Get-Mailbox" -- the same as user accounts).

If you could, you should try these 2 tests:

• This is happening for the Administrator staff role only, it seems? If you haven't tried yet, could you test adding the staff as any other role to see if they receive the email?
• Staff added to a calendar do not need to be in your tenant, and they do not need to be a Microsoft 365 account either. I tested it and it works for me. Could you try adding an external account to see if that account receives the welcome email? Note that the external account should be a valid Contact, or at least selectable from the dropdown menu as you type in its name.
• Try creating a brand new calendar, and add an "existing" staff and a "new" staff to it. See if they do or don't receive the welcome emails.

I'm mostly interested in the results from the 3rd bullet point. This would help further uncover more of the mystery.