It sounds like they did almost everything right. There are two fateful moments:
>At 05:41:46, the Captain asked the First-Officer if the trim is functional. The First-Officer has replied that the trim was not working and asked if he could try it manually. The Captain told him to try. At 05:41:54, the First-Officer replied that it is not working
At this point they were in stable flight and the trim wasn't that extreme. It's not clear whether "manually" here means manual electric trim or trying to physically turn the trim wheel. Up until this point they had correctly diagnosed the issue and taken the proper steps.
>At 05:43:11, about 32 seconds before the end of the recording, at approximately 13,4002 ft, two momentary manual electric trim inputs are recorded in the ANU direction. The stabilizer moved in the ANU direction from 2.1 units to 2.3 units. >At 05:43:20, approximately five seconds after the last manual electric trim input, an AND automatic trim command occurred and the stabilizer moved in the AND direction from 2.3 to 1.0 unit in approximately 5 seconds. The aircraft began pitching nose down. Additional simultaneous aft column force was applied, but the nose down pitch continues, eventually reaching 40° nose down. The stabilizer position varied between 1.1 and 0.8 units for the remainder of the recording.
They re-activated electric trim control but only slightly adjusted it. MCAS kicks in to send them nose down. There's no further pilot correction recorded. Unclear here if there is an airplane issue preventing them from adjusting trim or a pilot error.