I think you had an almost complete answer collating all posts, but one thing that was touched only on the surface was the minerals.
You may want to pull the construction table and check what minerals are required and for what. Worlds with native amounts of such minerals, may be good for the particular specialization, or at least this is what you have in mind: wrong!
If you want to specialize you have to chose worlds without minerals or part of the pops will be miners and you’ll have to produce and scatter all these mines around. Yes you can use Automines at double the price, but I would probably do that only for Class 1 worlds with all minerals or access to all minerals at more than 0.8 in the system. It’s like buying a house: Location Location Location!
Furthermore, you can always transport the minerals required to build the facilities using construction brigades (since you will be transporting minerals anyway for producing the interested goods), again limiting your pops effort to the given task.
In reality, you’ll find out soon that Aurora rewards massively the “tall” players as it is easier to handle the logistic, protect routes, systems and planets. And, to be honest, this happens to be true for many if not all SciFi settings out there. I would also expect, if space travels ever become reality, to be true in real life if we consider all we know about space today.
You can go wide, 100%, however, the investment in terms of resources may or may not really worth it, as it really depends of your RNG at system creation. Your most likely road soon will be 3 or 4 Earth like worlds with maybe only 2 having shipyards and most likely one of them you have “seized” from an NPR.
Finally, I think you may want to work on defining your colonies: Core, Outposts, Mines and then just split in 2 categories: Civilian/Commercial and Military. Once you do that then the only important size in terms of pops is to get to the 10M mark and unlock all potentials, goods, trade, and so on.