Lovely ideas.
Having wards be pulled into stuff you are doing as part of the teaching experience sounds a lot of fun.
Like if you are frequently running hostile schemes that you get events in which you deliberately teach your ward how to search for information or how to observe a target - even if you don't directly pull a 10 year old into your on-going murder plot.
If you construct holdings or buildings, you could deliberately get events tied to that.
Same for events relating diplomatic exchanges if you are engaging in some.
Of course combat training if you are versed in combat yourself.
And philosophical exchanges or medical apprenticeship if you have experience in those.
All those with massively increased chances if they fit the education focus set for the child.
That sounds very fun.
Exactly this type of thing, where wards have a chance to gain benefits (or harms) from activities your player and their court are doing, making for a rich and integrated thread of intertwined history.
Expanding on your example, if your player character is a shadow master, an event allowing you to use your ward to spy on your court giving intel benefit to your player character and an attribute increase to your ward, but with a risk of having your ward killed or beaten if caught.
If your court holds a lot of feasts, having an event during it where your ward is under the tables and hears something or finds something or gets drunk stealing wine, being another type of event.
Or if you are a torturer, you ward stumbling in on you in the act, and either being horrified and traumatised as a result, or awakening their own dark passenger.
Just some ideas to make the ward experience less "here's a completely random RNG event" and one more based off the environment they find themselves in, reflecting a real world development, rather than an RNG one.