As you said, when you use your icloud email to accept a Teams/Outlook meeting invitation, the meeting invitation does not include the meeting time and you cannot reply.
This is due to Microsoft's design. Only if your account is also a Microsoft account (including Teams and Outlook licenses), you can reply to the invitation and view the meeting time.
The purpose of this design is that after you check the meeting time and respond to the invitation, the meeting can be synchronized to your Outlook calendar, but the calendars of other mailboxes cannot be synchronized. I recommend that the organization invite your icloud email into the organization as a guest user so that you can view information in the Outlook calendar.
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