So, here is how I fixed it. Go into the adventure story in the picture to fix this little annoying Google-based fiction.
I also created my account long ago as @googlemail.com , but only @gmail.com shown in the drop-down list:

I tried @Peer and added myself to the project again with my full email address @googlemail.com . I did this through this URL:
https://console.cloud.google.com/projectselector/permissions/projectpermissions
(I am including the link because I did not find a way to go to this from the Google console to clear too clean for real links)
However, even after accepting the invitation, only my @gmail email appeared in the drop-down list on the consent configuration screen, @googlemail.com was still considered "Waiting for a reply" and, most importantly, it still did not remain:


So, I did the following:
- Fiddler Opened
- Click the save button in the consent form to enjoy the error for the last time (and also write it to Fiddler).
- Find the failed request in Fiddler (beautiful and red for us):

- Enable editing on the wrong request:

- Go to the
Inspectors tab and edit the supportEmail field to change your email address to @googlemail.com : 
- Right click on the wrong request, now it has been edited and go to
Replay -> Reissue Requests : 
The new request worked in charm, and now that I reloaded my consent screen, the settings were saved, but even better the drop-down value was the full @googlemail.com option:

So, I selected @googlemail.com and the save button worked successfully after:

(Although, apparently, I'm still waiting for my answer ...)

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