There's a decent chunk on the new official wiki about starbase upgrades here.

One important thing missing from there at the moment is discussion of options you can get to by clicking Sponsor Settings in the starbase management window. You can have starbases automatically request constructors to continue a chain of improvements you started (e.g. adding the next level of manufacturing or income booster).

The screentips in the starbase window are also decent; try checking them out for more info. One of my favorite new features is the ability to set a constructor design to send to a base. On large maps that can be really handy when you want to send your fastest, no-life-support model out to a distant base while using cheaper models to develop your core worlds.

Thanks for the tips.  I did finally realize that the modules in the upper right were constructor upgrades, and as someone pointed out, queuing one up orders a constructor from a nearby shipyard automatically.  Or it will just build instantly if you have a constructor already present.

I just started a new 1.82 game a couple of days ago, and although I have a cheap constructor design, and when I create a new star base the sponsor settings shows it as the selected constructor, if I request a new constructor for that star base it actually builds a more expensive one. If I click on the window to select a different constructor, then click back to my cheap one, it then works fine and from then on always builds my cheap one.

Has anyone else noticed that?

Right, it remembers it ok.  It's only the very first constructor.  Right after building the star base, the window says it's my cheap constructor.  Then I order an improvement by double clicking on it, and the window tells me it'll take 5 turns.  Then I cancel the improvement, switch to a more expensive constructor then back to my cheap one, order the same improvement, and now it says it'll take 2 turns.