It could theoretically be many different things:

- To assess what the satellite is capable of doing

- To geolocate where signals from Earth are originating

- To analyse patterns of multi-spot beam steering and bandwidth re-allocation

- Test denial of service attacks

- Test attacks where signals (or return signals) from Earth are manipulated (e.g. radar signatures faked)

- Test attacks where signals (or return signals) from the satellite are manipulated

- Eavesdrop on unprotected communications

- To waste fuel on the target satellite as it maneuvers to avoid any of the above (even if nothing is attempted)

- To make the other party second guess their technology for no good reason, lowering their confidence in its accuracy or usefulness

I'm sure there are plenty of other possible explanations which could be added to this list.

Satellites have maneuvering thrusters with a very limited supply of fuel that will last just long enough for the designed mission-life of the satellite. Approaching the satellite will cause an unplanned maneuvering burn that effectively shortens the life of the satellite.

For military satellites, proximity avoidance is fully autonomous. Therefore, you can design a satellite to chase other satellites to fuel exhaustion. I’ve been told this is an actual thing.

Getting a close look at it, and seeing what it can do. For instance, seeing if it's capable of precisely the evasive behavior that it apparently demonstrated.

About the only thing I can think of is potential access to narrow beam signals, and or leaking signals like snooping the satellite.