You just described a few different sub-fields of computer engineering:
1. Processes, which involves lots of materials science, chemistry, and low-level physics. This involves the manufacturing process, as well as the low-level work of designing individual transistors. This is a huge field.
2. Electrical circuits. These engineers use specifications given to you by the foundry (transistor sizes, electrical conductance, etc.) and using them to create circuit schematics and physically laying out the chip in CAD. Once you finish, you send the CAD file to the group from #1 to be manufactured. Modern digital designs have so many transistors that they have to be laid out algorithmically, so engineers spend lots of time creating layout algorithms (called VLSI).
3. Digital design. This encompasses writing SystemVerilog/VHDL to specify registers, ALUs, memory, pipelining etc. and simulating it to make sure it is correct. They turn the dumb circuit elements into smart machines.
It's worth noting that each of the groups primarily deals with the others through abstractions (Group 1 sends a list of specifications to group 2, Group 3 is given a maximum chip area / clock frequency by group 2), so it is possible to learn them fairly independently. Even professionals tend to have pretty shallow knowledges of the other steps of the process since the field is so huge.
I'm not super experienced with process design, so I'll defer to others in this thread for learning tips.
To get started in #2, the definitive book is the Art of Electronics by Horowitz & Hill. Can't recommend it enough, and most EEs have a copy on their desk. It's also a great beginner's book. You can learn a lot by experimenting with discrete components, and a decent home lab setup will cost you $100. Sparkfun/Adafruit are also great resources. For VLSI, I'd recommend this coursera course: https://www.coursera.org/learn/vlsi-cad-logic
To learn #3, the best way is to get a FPGA and start implementing increasingly complicated designs, e.g. basic logic gates --> counters --> hardware implementation of arcade games. This one from Adafruit is good to start: https://www.adafruit.com/product/451?gclid=EAIaIQobChMIhKPax..., though if you want to make games you'll need to pick up one with a VGA port.
Silicon design & manufacturing is super complicated, and I still think that it's pretty amazing that we're able to pull it off. Good luck with learning!
(Source: TA'd a verilog class in college, now work as an electrical engineer)