I personally have only thought bits and pieces on this, but felt it worth saying.
I think that background actions we never see, like dwarves having conversations that leads to two of them getting in a romantic relationship and later married, should get tweaks
I'm talking tiny details, like a dwarf that is extra persuasive, convincing another dwarf, or two, to convert to their deities or deity
This would cause the prior deity or deities, to be listed as 'former deity', and a change in the description text
If the persuasive dwarf does it enough times, converting others, they could be granted a 'boon', if adding something like that was approved (I don't think this bit is necessary, but I thought it up in regards to 'what consequence would this have')
Little fluff things like that, or maybe even a dwarf having thoughts of leaving to be an adventurer (this happening more often in dwarven kids and the like)
If a kid going out to adventure did "become a thing", it could have traits similar to the dwarven caravans that could be implemented. It could cause a raise in certain statues being made, or fame of the fort, maybe the adventurer sending back the fruits of their travels (Like exotic/rare weapons and items you aren't normally able to craft, or exotic pets that are already tamed)
EDIT: Also, this could potentially extend to the category of music
In conversation, two dwarves could eventually decide to start a 'jam session', similar to a party, where they and a couple of other dwarves (if any are nearby that fit the qualifications) begin playing instruments they have on hand
This could cause a mood benefit for dwarves passing by, hearing music, or hearing music they enjoy
This could extend further, to a dwarf becoming a 'bard', giving mood benefits and possibly increasing worker productivity/speed
Or dwarves playing music at a party, or if a building is designated as one, a "concert" being held at an "amphitheatre" (which could also hold Dwarven Plays, where a small number of dwarves perform rituals that relate to religious or historic events)
Again, most of this just gives fluff details, and nothing that impacts the game too heavily at least in theory