I have observed that, in my case, invitations that appeared to not be delivered were actually being delivered. In my case, Homekit stopped working one day. I suspect it was the 16.3 update but it may have been an earlier update (was there a 16.2.x?). Anyway, I had to nuke my entire Homekit set up and start over. I was not a happy camper. Nevertheless I spent at least a couple days troubleshooting and rebuilding.
When I tried to invite my wife to the rebuilt home, the invitation was received but when she accepted the invitation, she was given an error about a conflicting home name. I have wiped the home from my phone entirely several times to try and resolve the issue including using the Apple mobile profile that nukes the Homekit database in iCloud. I have also power cycled my phone, her phone, and my hub several times. Nothing I have done has fixed this issue though nuking the database or changing the name of my home made a slight change during the acceptance phase. My wife no longer receives a message about a conflicting home name. Rather, accepting the invitation shows a "joining home" message with spinning gear that eventually disappears, the screen refreshes and taken back to the no home screen.
Along the way I noticed that the invitation notification on her phone displayed an address from the mac.com domain. I thought that was peculiar because I never use that iCloud account when I set up a new device. The Apple ID associated with the iCloud account that I am signed into on all my devices is different because years ago Apple forced everyone off of their mac.com and icloud.com email by insisting that your Apple ID email address could not be the same as your Apple ID. I looked at my contact info on my wife's phone and she had my mac.com address in the contact info along with my other addresses. So, I removed my mac.com address from her contact info. I deleted the invite from my phone and invited her again. After the change to her contact info for me, the invitation notification did not appear on her phone. I did however notice a slight change to the ellipses in the top right corner of her Home screen. When I clicked on the ellipses and selected the Homekit Settings, the invitation appeared on the Homekit Settings screen. The invitation was described here as coming from an unknown source with a warning about accepting an invitation from someone you do not know. When my wife accepts the invitation, the gear spins and the invitation is never completed.
So, I do not have a solution yet but perhaps my experience might shed some light on where to find your missing invitation. If you do find it, I would be interested to know if you are able to accept and then complete the invitation.