Is there like a programming language of some sort where a compiler converts syntax into circuitry layouts?

You are looking for something like System Verilog (Or VHDL).

Both these languages let you describe hardware. They can both go down to the circuit and transistor level, but people won’t write that by hand. Rather, they will write code that is a description of digital hardware (flip-flops and the logic between them), and then let tools synthesize their description down to individual logic cells and simple functions. Often, chip fab houses have “standard cell libraries” that implement the most common logical functions, and the tools stich them together based on the higher level description.

Then there is all the verification that needs to be done, not just verification that the design is doing what it needs to do at all times, but that every individual chip is make correctly. Defects do happen, and you want to find them as early as possible in the process.

Lots and lots of expensive tools and specialized knowledge! A good middle ground are FPGAs. These are special chips with lots of generic logic building blocks, and ways to programmatically make connections between them. You can write the same VHDL or Verilog for FPGAs, butt the tools map the logic to the FPGA vendor’s chip instead.These still require tools and specialized knowledge, but much cheaper than a fully custom chip.