I use Gmail for my work email and calendar, and I've added the Gmail account to the macOS native Calendar and Mail apps.
All is working well on the Mac. When someone invites me to a meeting I see the invite in my Calendars 'inbox' view, and can choose to accept it, etc.
On iOS it's a little weird, however. I see the meeting in the calendar day view, where I can see it's not yet accepted/maybed/rejected, however it doesn't show in the iOS calendar 'inbox'.
I do see all my invites in both iOS and macOS in the replied view under inbox.