I’ll try to bullet point this…
-Like you and others—this is where terminology gets confusing—I have multiple color-coded “calendars” within the Apple Calendar app: Appts; Meetings; Tickets; Zooms; Travel, etc.
-One of those “calendars” is “GMail”, created automatically when I added my Google to Accounts.
-My Gmail account has been my primary email for many years and that’s where invitations are sent.
-When I receive an invite, it automatically goes into that GMail “calendar” within Apple Calendar.
-The Problem: GMail invites cannot be switched to Meetings, Tickets, or whatever is appropriate. My Apple “calendars” do not appear on the drop down menu in the event.
-They cannot be edited, either, if I want to change the title, color, or add travel time.
-In addition, if I manually duplicate the event and delete the original GMail invite one, it sends a “Decline” to the sender—even if I’ve previously accepted it.
-Downloading the ics attachment doesn’t help; the issues are the same.
There should be a way to integrate fully editable GMail invites into the “calendars” in Apple Calendar. That’s what I and others are looking to do.