Is this a question specifically about this community, or generally about how chatting with moderators can work?
There does seem to be a weird bug that you’ve uncovered about the number of members the moderators group seems to have - can you start a Contribute > Bug topic? The automatic groups like admin and moderators are special and do have some unusual behaviors that can get confusing, and we’d like to improve that.
Regarding this community, I’d say we’d prefer to not have members start chat with all of us. That will get too noisy and chaotic. If you have a concern about a topic, flag it and we will see it and one of us will respond. Also the flagging system will help by unlisting topics that need to be unlisted, letting us quickly delete spam posts and accounts, etc.
If you want to reach out to us about something else, then write @moderators a PM.
Starting a topic here in Contribute > Site feedback is also fine if you have ideas for improving how we manage this community.