I should know more about what's happening under the hood.
You've just identified the most important skill of any software developer, IMO.
The three most valuable topics I learned in college were OS design basics, assembly language, and algorithms. They're universal, and once you have a grasp on those, a lot off programming language specifics become fairly transparent.
An area where those don't help are paradigm specifics: there's theory behind functional programming and OO programming which, if you don't understand, won't impeded you from writing in that language, but will almost certainly result in really bad code. And, depending on your focus, it can be necessary to have domain knowledge: financial, networking, graphics.
But for what you're taking about, those three topics cover most of what you need to intuit how languages do what they do - and, especially C, because it's only slightly higher level than assembly.
Assembly informs CPU architecture and operations. If you understand that, you mostly understand how CPUs work, as much as you need to to be a programmer.
OS design informs how various hardware components interact, again, enough to understand what higher level languages are doing.
Algorithms... well, you can derive algorithms from assembly, but a lot of smart people have already done a ton of work in the field, and it's silly to try to redo that work. And, units you're very special, you probably won't do as good a job as they've done.
Once you have those, all languages are just syntactic sugar. Sure, the JVM has peculiarities in how its garbage collection works; you tend to learn that sort of stuff from experience. But a hash table is a hash table in any language, and they all have to deal with the same fundamental issues of hash tables: hashing, conflict resolution, and space allocation. There are no short cuts.