Still playing this.(can't stop. help)
Started doing a the main quest, and ran into a brick wall when my current interrogation target, possibly the last one I need for the first mystery, has a Withdrawn personality. That means you cannot break their emotional guard(limits favor to 60, need 100 to get their secrets) with anything except the dog's 100 Intelligence ability. Except that my dog's Intelligence was nowhere 100 and I hadn't seen them training for some time.
Did some testing and research, and found some things about how to manage your pet. They'll only train if their leisure stat is full, and training is seemingly only effective if you do not interrupt the session(despite the dog saying otherwise). At 100 nutrition, a training session seems to take 20 nutrition and increase Intelligence by about 6. Might be variable.
Increasing leisure is a bit tricky. Obviously, your dog can't be doing work around the sect. I may have screwed myself a bit by having the dog's labor training set to maximum for most tasks. Even if minimized, the dog will stand there talking about the work. You can interrupt that until the dog takes an action to restore leisure or train. So far, I've found that "(Playing) Take a Rest" restores leisure, but "(Playing) Take a look around" and "Follow *disciple*" do not. "Missing", where you have a cultivator on an adventure and the dog is asking about them, restores a lot of leisure, almost enough to fill it in one action.
I also just started the Thousand-year Tide events. Some fun will be heading my way soon.