According to Ballotpedia Boudin was leading from round 1 and the transfers helped Suzy Loftus to catch up, but not enough.
After Round 1 Boudin was leading by ~8,800 votes and by the final round his lead had melted down to less than 3,000.
https://ballotpedia.org/Chesa_Boudin
Okay, thank you. I misremembered some of the details of that election. Ultimately, though, Boudin’s election was the product on ranked-choice, as only 45% of S.F. voters ranked him 1st, 2nd or 3rd. There’s a good explanation here:
https://www.city-journal.org/instant-runoff-voting