On the other hand, if you look carefully at the landing video, it looks like they did a three-engine landing boost on the other boosters: https://youtu.be/BBA7su98v3Y?t=517 So they have definitely learned something valuable in that landing incident.

Interesting. Looks like a 1-3-1 burn (start with 1, ignite two more for a bit, then finish on a single one).

I wonder how much longer the '3 engine burn' was for the GovSat launch last week that did a 'water landing'

Cool. I'd assumed they only did that with the centre core, but you're right.

Is the normal landing a 1-engine landing? If so, is the advantage of a 3-engine landing that it requires less fuel due to having a much shorter 'suicide burn'?

Yes, and yes. The less time you're in the air, the less fuel needed to counter gravity's continual pull, so the most efficient landing burn is basically the highest acceleration you can handle without coming apart such that your velocity hits 0 as your altitude does.

What’s a “suicide burn”?