Automail has various widgets for creating status posts, posting replies, updating ratings, and updating episode counts.

When you edit one of those, Automail sends the change to anilist.co via the official API.

Automail also requests data from Anilist for many of its function, using the same API.

In a specific case, and only if enabled, Automail adds some anime/manga data from myanimelist. This means fetching the generic myanimelist pages, nothing else, so Automail has no access to your myanimelist account if you have one.
Automail does not send any data to myanimelist.

As all of this happens on the Anilist website, this is all data that Anilist has access to anyway.

Automail does not collect and send data to anyone else.