Their retraction note is very brief, and simply states the information was wrong.
Edit: pasting the entire message
> WARSAW, Poland (AP) — In earlier versions of a story published November 15, 2022, The Associated Press reported erroneously, based on information from a senior American intelligence official who spoke on condition of anonymity, that Russian missiles had crossed into Poland and killed two people. Subsequent reporting showed that the missiles were Russian-made and most likely fired by Ukraine in defense against a Russian attack.
https://apnews.com/article/russia-ukraine-war-zelenskyy-kher...
He posts the received tip at 1:32, mentions his doctors appt at 1:38. Lisa says sending alert at 1:40.
<span class="Timestamp Component-root-0-2-39 Component-timestamp-0-2-38" data-key="timestamp" data-source="2022-11-15T18:41:15Z" title="2022-11-15 18:41:15 - Tue Nov 15 2022 13:41:15 GMT-0500 (Eastern Standard Time)">November 15, 2022</span>
which exactly corresponds to the 1:41pm "alert sent" message in the screenshotted Slack conversation. So they did indeed publish it based on this Slack thread.
[0] https://apnews.com/article/nato-ap-news-alert-europe-poland-...
Seems like an optimistic assumption.