Archaeology sites and colony events are supposed to take the place of anomalies in the midgame. Colony events tend to be a bit more trouble than they're worth though* and because they always spawn super fast after popping the colony down they're functionally also an early game event type.
More colony events that only happen after the colony has reached a certain age threshold (and aren't all ways to just screw the colony over) and ones which happen on conquered and/or integrated colonies which have different options and outcomes for different government types would be good. And these don't need to be world changing events, they can have the kind of minor outcomes that a lot of weaker anomalies do as well as more permanent changes (modifiers, new features, etc.), just something to interact with as colonies grow and change.
* Let me take a moment to expound my hatred for the Abandoned Terraforming Equipment colony event. Of its four possible outcomes, one is always negative (Tomb World, colony dead), two are negative in 75% of cases (random planet type has 75% chance to be less habitable than it started, plus one may kill the colony with monsters if you didn't prebuild armies expecting them because the colony is new and weak), and only one is genuinely positive.
So your choices are to gamble on a one in three chance of a positive outcome (plus spend on armies, almost certainly in the early game still), or to accept a permanent -10% happiness malus to the planet which you can never remove, even if you do complete terraforming on it later. The event sucks, and it's almost guaranteed the first time you settle an off-perfect habitability planet. If that's a very early colony for you the setback of having it go dead or to 20% hab can be amazingly annoying. It's almost never worth taking the risk of actually doing the project.
It's not the only one, the Pheromones event chain has basically no chance of a good outcome and a bunch of costs and penalties along the way so the only sensible way of dealing with it is to shut it down at the first opportunity.