Not to sound snippy, but how do you define projects in your world, and how do you benefit from having 21 of them open at once? How many do you interact with in a typical day?

That setup is so far removed from my day-to-day experience that I'm genuinely seeking understanding here. At most, I typically have 3 or 4 open "projects" at once, and those would be fairly tightly related (like, a server codebase and a couple of clients for it).

I'm not going to go into my specific needs or project setup, but even with 4 open projects, IntelliJ requires 4 open windows! That's asinine when both NetBeans and Eclipse allow me to decide how many projects I want open within a given IDE window. It's the biggest reason I only use IntelliJ when writing IntelliJ plugins.

Even then, I keep these related codebases as separate modules inside a single project.

Have you looked into setting up your projects as modules? I have dozens of modules in a project with no issues. If the projects are related there are benefits like source code linking too.