Could the number of space docks a planet has be directly determined by the planet's population? Or do you want it to be a decision of the Player?

If you want to implement planetary "buildings" without going into a planet-specific interface, maybe this could be done by having a construction side panel that can be opened when looking at the galactic map. Construction of a new thing at a certain planet by clicking and dragging the thing from the panel onto the planet on the map. Information about what planets that construction is viable on could be relayed via changes in the map while the item is being dragged around (if it can't be built on a planet, that planet turns red, dims out, etc)

don't want to check for building slots

Do you need building slots? I would argue that every planet (even a moon) is large enough to hold every arbitrary amount of buildings. Every reasonable amount and any amount that you could possibly fit into the computer's main memory, anway. Even the world's largest university isn't a challenge to fit on a continent with the world's biggest hadron collider and two dozen military research facilities and 200 pilot schools. As long as you have the resources to build these facilities, I see no reason why room should be an issue (when the scale is "planetary").

Thus, I would just let the player build these special buildings whereever they want, and list them in a location-agnostic directory/roster for access. Of course the player still has to click on the "planet level" in some way once to decide where to build that special building. But this is important, and it's not something you can (or should) remove. After all, it's tactically an important choice where your stuff is found. If both your university and your rocket research center are on a planet deep in the enemy territory and the enemy blows the planet up, then... well, then the location was a bad choice.

I like the organizations. One thing is that organizations could themselves be builders. (So each planet handles its own build queue and decisions, but the presence of particular guild can influence their progress and decisions. A space elevator might be a pipe dream for a provincial backwater planet, but the existence of the Skyhook Guild brings it within the realm of possibility.)

I'm thinking of the guild of hydrodynamical engineers that went around Europe in the Middle-Ages (-ish) to build canals and such. It wasn't that each city would have a hydrodynamical guild; there was just (if I remember correctly) one and they traveled where they were needed.

So if the goal is to have some control over whether your empire builds a lot of fuel depots vs. universities vs. whatever, you could do it by chartering organizations that build these. You just know that they're out there doing their thing, and doing it better than the planets would manage to do in their absence, but you as the emperor don't necessarily know or care where. At the point that you have 200,000 planets, they might be founding a new planetary university every week, but you don't have to be notified except regarding the big picture.

Also, it gives you something to have audiences about. Organizations would have liaisons in the emperor's court, and that lets them potentially beg you for stuff, get into fights with each other that you have to adjudicate, etc.

How about:

A few "Orders" already exist, and others come into being through events. They can't achieve anything without patronage, though.

When you take over a planet and are choosing what to do with it, there's one more option: to grant it to an Order. The economic output of that planet then goes into their budget, which they use to do their thing, whatever that is. An Order doesn't have a "level" and isn't part of the imperial budget, and it doesn't scale to the size of the empire. It just has some number of planets held in fealty, and uses the resulting income to go around building hospitals or whatever its mission is.

However, even though they don't automatically scale to the size of your empire, there's still a good potential for correlation, in that the decision to "level up" an Order (that is, grant it a planet) is present at the exact point at which your empire expands (when you grab a planet). So if you're diligent in granting (say) every fifth planet to one of your favored Orders, their ability to serve your empire will expand at about the same rate that your empire is expanding.