Next, you will eventually ask the question of how to make a production board, where you may go down the rabbit hole of programming the AVR directly (the microcontroller), which I recommend as a jumping off point into raw microcontrollers and using an ICSP which an Arduino UNO can also do for you.
Somewhere along this path, you will want to gather some more advanced knowledge of circuits and DC fundamentals. Pick up a set of 7400 logic chips and learn how logic gates work from the lowest level possible as well as op-amps, comparators, etc.
You'll find every chip (IC or integrated circuit) speaks in either a protocol/bus or just logic levels (pins going high or low). When more than a bit or so of data is required to be transferred, ICs will implement a general-purpose digital interface like I2C (most common), SPI, or UART. There are some additional ones like I2S (for audio), 1wire (for one wire communication), CAN bus (what your car likely uses), and there are some more advanced ones like PCI (the same kind bus your PCI slots in your computer uses), MII (media independent interface), etc. Most of the time, you are just connecting together devices on a bus (for example I2C can support multiple devices because it's addressed) or finding ways to convert one to another (for example, you might want to communicate in RS232 via your UART bus).
There is also analog which is a whole different beast.
This is all a big simplification, but honestly it's not that unapproachable these days, just start small and build from there.
Had it not been for the stock shields in the Arduino world, I probably never would have gone down the rabbit hole as far as I did. That's meant as a compliment.
Beyond that is outside of my experience, but building CPUs seems to be a bit of a hobby these days. I have found Ben Eater's videos to be enlightening. I think he built a CPU at one point, but even the tutorials using a 6502 are useful since he reasons through the construction of supporting circuitry. I haven't watched much of James Sharman's work, but he is building a CPU and carrying it through to the PCB stage. The videos I've watched (related to producing video signals) included reasoning through the design process.
EDIT: I'm not suggesting the microcontroller route since it sounds like you want to explore how to build a CPU. A microcontroller is a CPU with integrated memories and peripherals, which is too high level. (Granted, if you aren't interested in a particular aspect of CPU design you can use a microcontroller to fudge it.)
PCBs aren’t a necessary step unless you want to make many copies of your work. They basically reduce the wiring you need to do & allow for a more compact circuit than a breadboard.