If a player tanks their standing and has a capship on follow, the player's standing is not transferred to their capital ship. In fact, if that capital ship is then attacked in a monitored/guarded place where that player is tanked (hate/kos), that player gets a defense flag against anyone shooting their capital ship.

Don't think that's a bug, standings should only be transferred if the player docks in their capship. Similar to how if you have a defense flag on someone and they dock in a capship, you get a defense flag on the capship too.

I guess it would be nice to have some clarification on whether the devs consider this a bug, because to me it doesn't make sense that a player would be KoS but their capship would not (regardless of whether they dock with it)

It appears to be a bug. Basically, TempKoS was probably the main focus of testing at the time when it was implemented, and it appears that long-term standing changes are not properly transferring immediately.