Thanks.

> You said "making this e-mail address public" in your question - it's worth noting that binding a 3PID does not publish it in a public list; instead, it means it can be used as a key to look up your MXID for users who already know your email address.

The domain part of e-mail addresses is public anyways due to certificate transparency, meaning that an interested party would only have to enumerate the local part to find all e-mail addresses from a specific domain used by Matrix users. In this respect, the lookup answers the question "Does this address exist?" and as such makes it public.