Granted I'm only 3 episodes in but it doesn't seem like Ishikawa has a family first of all and Kindaichi isn't really his assistant per say
Is there some background to this show I should know?
Usually, synopsis get wrong all the time- misleading facts- and I'm afraid this show is one affect by them.
They use synopsis more for "bait" than anything else actually.
But let's see if I can get more straight to you than the faulty synopsis per see.
I've finished the show already, watching when was around in 2020 so I might not remember clearly everything and this anime it's not exactly "memorable" but, honestly, if you're into detective/mystery kind of shows this is one of the few that actually has some interesting turnovers that I can remember lately "narrative wise" (let's just put like this).
About their background, as you initially ask, I don't remember about Ishikawa family either. Ishikawa, most certainly, is the most intriguing character in the show but I think that if you stick with the premise that he is "selfish", "eccentric" and, as I would say, "hard to read" it would be for the best for the plot play around with you with this immediate portrait. His author's motive while solving the cases is what drives this show.
Kindaichi is a teacher and heartwarming person... really caring but, still, I don't see him as a "saint" or selfless at all. I guess that we could simply label him as a naive person and I'd call it.
I don't see, at all, their background playing much for the impact of the show, at least, regarding their family. I guess you could focus just how is their bond and focus in their interactions and you would be fine.
Btw, Ishikawa seems to take a lot of Kindaichi kindness and they have some drama in their relations. Sometimes, Ishikawa seems to plainly exploit Kindaichi and I was baffled at the beginning that, despite his reactions, it didn't seem to bother much him (I, also, would recommend you to focus in this cuz, sometimes, the show doesn't give the amount of screen to explain as much as I would want this).
I didn't read the original source and, like many adaptations, this could be just one of those which doesn't make a name for the "real" thing.
Although I think the show itself could be a little bit clearer for what it was trying to develop, it was a good one and I think is slightly underrated if you don't mind me saying.
I'm not sure if this will do for you but I hope that I was, at least, helpful to "guide" possible insightful moments that wasn't highlighted in the show as I think it should- this in the upcoming episodes for you.
PS: thanks for the discussion thread btw, I nearly forgot about this show 😑