> How does getting there more slowly mean more science at the destination?

Mass. Small payload fast. Or large payload slower. (Also flyby vs. orbital insertion. If you’re going fast, you don’t get to loiter.)

The trade-off for a given rocket is more spacecraft (and instruments to do science with) vs getting there faster.

Maybe slower speed means more time spent in close proximity. Moving things don't exactly stop on their own in space. Or maybe they wanted more stuff on there

It’s the latter.

Delta-v is a scarce resource!

Depends on what "more science" means, but one factor is that going fast means you need to burn a lot more fuel to slow down so you can get into orbit around the target planet.

The mass of the fuel spent on breaking could be spent on other things, like extra instruments, or fuel for thrusters so you can orient more often and stay in orbit longer. For example, the Galileo[1], Cassini[2] and Dawn[3] missions ended primarily due to the probes running out of fuel. Perhaps not the best examples since they all had quite long runs, but still, more thruster fuel would probably have meant even longer missions.

[1]: https://solarsystem.nasa.gov/missions/galileo/timeline/#jour...

[2]: https://solarsystem.nasa.gov/missions/cassini/mission/grand-...

[3]: https://www.jpl.nasa.gov/news/nasas-dawn-mission-to-asteroid...

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