So, something I just discovered from the project I was working on about:
gam print groups query ""email=$($_.email)"" allfields
It appears that the above query is case sensitive in regards to the email address.
However, the results of that query (and any other I've found that returns Google Groups email addresses) returns the group email address in all lower-case.
This means that when I took a list of all users in our top-level OrgUnit, and listed all the groups those users were members of, and sorted those group emails with the -Unique option to remove duplicate group email addresses, then fed that list of (all lower case) group emails through the above query, it failed to find the settings on any groups which had upper-case letters in the email address.
Not sure how I could FIND those groups' correct case-sensitive names, other than looking in the Admin console manually (not gonna happen for over 500 groups) so I looked for another way.
The query parameter can take "email:<emailStartsWithString>*" with a colon instead of an equals-sign, and ending with an asterisk - this query is NOT case sensitive, and I figured if I put the full email address with the asterisk appended, I should only find the one group, since we never registered
ourdomain.com.ourdomain.com as a domain in our Google tenant ;)
Gotta say, that one went un-noticed for over a week - no errors in the logs, since a query that returns zero results is not actually an error condition.
It also blew my mind that
gam info group <emailaddress>
returns lower case, regardless of what mixture of upper/lower case I put in the email address, when that's not the case stored in the system, and that there would be any query that would be case sensitive when all results seem to actively lower-case the addresses before returning them.