Darn it, Kyoki. I know you counted on Tom to interact with you. I was counting on the very same. That said, sorry.
By this point, most of what Miharu needs is maintenance work and a degree of jury-rigging to get things running... because the damage taken isn't really something that can be fixed out of spacedock.
Many sprites are probably busying themselves fixing various 'things'. This said, you can choose for Rin to join in (you're welcome to make suggestions on what you think would need attention post-battle), but seeing new supplies coming in Rin could also help arrange what comes in, help fix some of the damaged armors (Wish is still kinda messed up, for example) and such.
Seeing no rigid scheduling was made yet, it seems up to your character to determine where her talents would be the most useful. Either you can start something on your own, or approach another player character and ask if you can help out.