From the save you gave me, it opened on a Tuesday day, with Kate Affection 1 Corruption 0.
I did the bar minigame that night, made sure to listen in on her and Thomas upstairs at midnight.
Bar minigame Wednesday night, made sure to listen in on her and Thomas after.
Bar minigame Thursday night, made sure to listen in. At midnight started the unofficial relationship. Kate Step #5
Repeat Friday, nothing new.
Repeat Saturday, was able to tell Thomas to stop blackmailing, and brought Kate to MC's room in the Inn (I got the key from Thomas back on Tuesday night), accidentally hit go further, instead of making her cum. Wasted a night on that front.
Repeat Sunday night, made her cum in MC's room at the inn.
Repeat Monday night, at midnight Kate called Clare into her area of the room to make MC and Kate's relationship official.
Tuesday night, eight days later, did bar minigame Old friends came in.
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So I ended up doing the bar minigame eight times, which seemed to be a high amount, but maybe that is normal. Normally I am not concentrating on only doing it and skipping everything else. But then again starting with Kate from the beginning, with a save file that already has the catdoor in a renovated MC house is a much different order than I am used to playing. You didn't do anything wrong, it's just that "Old Friends" is a level 8 quest, while you already completed almost all the level 25+ quests.
I'll give you the save if you want it, but I don't think you should. I made a couple of choices that effect things (Kate's corruption is at twenty, no Thomas blackmail and told her she should dance in the bar) and advanced other questlines, mainly Claire. Plus you aren't done with the bar minigame so you should make sure you have a good handle on it.