In Y1, you could miss sidequests. I think after that you couldn't miss them anymore, but in Y4 at least you could potentially fuck up a sidequest. However, it still counted towards completion rate. I don't think there's an option to even fuck up a quest these days though.
Yakuza 3 was the last time you could screw up side quests and fail to fight Amon because of that. 4 and up they tweaked it so it was no longer the case. Mercifully Kiwami follows that lead and you can no longer fail side stories (can't wait for Kiwami 2 to implement this as well).
However, one thing I remember regarding side stories and the completion list:
There is a challenge on the completion list to get a certain number of weapons. Most can be bought or won from the arena however you need to be careful as a small amount are also rewards from side stories by getting the best outcome. You don't need to get every weapon in the game, so you can afford to miss a couple from side stories but just keep this in mind, unless that is you enjoy grinding for points in the arena over and over!
And speaking of arena points grinding. Best way to do so (once you aquire the Tiger Drop and have the Dragon style pretty much maxed out) is to go into the last arena tournament and really abuse the Tiger Drop. You clear enemies out in 2-3 hits if your lucky and get a shit ton of points.