There are/were quite a few CPUs where the program counter is one of the general purpose registers.

For example, https://developer.arm.com/documentation/den0013/0400/ARM-Pro...:

“The ARM architecture provides sixteen 32-bit general purpose registers (R0-R15) for software use. Fifteen of them (R0-R14) can be used for general purpose data storage, while R15 is the program counter whose value is altered as the core executes instructions. An explicit write to R15 by software will alter program flow.”

Similarly, the PDP-11 used R7 for that. https://en.wikipedia.org/wiki/PDP-11_architecture: “The CPU contains eight general-purpose 16-bit registers (R0 to R7). Register R7 is the program counter (PC)”

I’m not aware of any CPU where “every register could be the program counter”. Such a feature also feels weird to me from a design view because I think it complicates the hardware with few (code might be smaller for a limited set of jumps) benefits. Maybe you’re confusing that with the ability to jump to whatever address is in any of the general purpose registers?

EDIT: I just saw a comment mentioning the 1892. It indeed had that ability. https://en.wikipedia.org/wiki/RCA_1802#Registers_and_I/O:

“The SEP instruction can select any of the 16 registers to be the program counter. The SEX instruction can select any of the 16-bit registers to be the index register.”

That description does not match the RCA 1802 [1] perfectly, but it is probably the best known microprocessor (not a microcontroller, though) without a dedicated program counter. There are a lot of misconceptions about it floating on the internet, so I would not be surprised to hear it described as you did.

[1] https://en.wikipedia.org/wiki/RCA_1802

This might have been the PDP-11.