iphone calendar invites not showing in recipient email inbox

One specific iphone user is sending me (specifically a gmail a/c) invites from their iphone calendar but those invites are not getting into my gmail inbox and also not my google calendar. This gmail a/c of mine happens to be my appleid as well. By chance this morning I saw on my mac a notification of one of those invites and when I clicked on it it opened in the mac calendar (which I never use) and that calendar shows the other invites that I thought were missing (ie not showing in my google calendar or gmail).

Question: Is it possible that the iphone calendar sends invites directly to an appleid instead of the email address that is the appleid? And how can that be changed so it sends the invites to the email address instead?

I have also verified the following to be true: using my iphone calendar (linked to a MS 365 a/c) I sent an invite to the same gmail in question and that invite showed up both in my gmail and google calendar. So the issue appears to be how the iphone calendar of that specific user is sending the invites.

Btw I want these invites in question to show in my google calendar instead of my iphone calendar so as they are not comingled with my MS 365 stuff.

That specific user is using an iphone 14 whereas I'm using iphone 13 pro if that makes a difference (which I doubt).

Thanks