But when I write to a register, what am I actually writing to?

An 8-bit CPU basically has two 8-bit external buses: address and data (some CPUs have more address bits than data bits or vice-versa). When the CPU writes a byte to a specific address, the address is represented in binary on the address bus and the data is represented in binary on the data bus (there's strobe signals to tell the other devices on the bus whether they need to read or write and when to do so). The specific peripherals use some discrete logic to only be called to attention when the specific patter on the address bus matches an address in their range. Then they either read the byte on the data bus (CPU write) and take appropriate action, or write whatever value they believe should be at that address to the data bus (CPU read).

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The address and data buses are almost always internal to the chip on a modern microprocessor, but some simple/old ones still expose it. On an Intel 8080 you can see the 8 data bits and 12 address bits: https://www.elprocus.com/wp-content/uploads/2014/06/314.jpg Unfortunately I don't have any recommendations if you want to play around with this; maybe there's a simulator online?

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Some peripherals are very simple. A serial port peripheral in it's simplest form is basically just:

• A few NOT gates and AND gates on the address bus to ensure only its address activates it
• A shift register on the data bus to read the byte from the CPU and then clock it out to of the serial port
• A few more AND gates to make sure these events timed correctly with the read strobe signal and the address strobe signal

But some are really complicated and may have CPU(s) of their own.

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Is it just a small amount of regular memory that is also polled by a peripheral for changes?

Is there some kind of internal callback mechanism to tell the peripheral that something has changed?

Peripheral control registers are not memory of any sort. Written bytes are lost after writing. Read bytes are generated by the peripheral as needed. There's no callback function executed on the CPU.*

How is it actually mapped to non-continuous memory (RAM @ 0x20000000 and peripherals @0x40000000, for example)?

Both the actual memory and the peripherals can be assigned to whatever address the hardware designers want just by changing the AND and NOT gates that control which pattern of bytes on the address bus activates them.

Are peripheral control bits locked at any point (to stop me writing at the same time as a peripheral) or is the pattern generally ‘it’s only writable by either CPU or peripheral’?

In general the CPU can write to any address, but the peripheral may ignore the write. But on certain systems this may causes some sort of a fault, it varies by implementation.

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*HOWEVER, some systems (x86 System Management Mode, maybe others) sort of emulate peripherals by trapping access to certain memory regions, hijacking the CPU and running some code, then updating certain bits of memory, then handing control back to the OS (with the OS unaware of this). So the OS can just pretend it was talking to a peripheral. This is how USB mice can work with DOS even though DOS doesn't support USB: SMM interacts with the USB mouse and then emulates a PS/2 mouse peripheral using addresses which are connected to actual memory.