More searching finds the Magitronic 20B33 manual for a "Super 286 Baby Mainboard", which says on page 10:
- When switching speeds externally:
A mechanical switch is installed onto JP7,
JP7 in the OPEN state provides Low speed, when CLOSED, it provides High speed.
- When JP7 is OPEN, the clock speed can be switched by using the keyboard. When using AWARD BIOS, keys CTRL, ALT and - (minus) are pressed simultaneous) to switch to High speed. Keys CTRL, ALT and + (plus) are pressed simultaneously to switch to Low speed.
- If the power is turned on while JP7 is OPEN, it will turn to Low speed. If JP7 is CLOSED, it will invalidate the keyboard operation and will switch to High speed at all times .
- When using PHOENIX BIOS, keys CTRL, ALT, and \ are pressed simultaneously to switch speeds.
So that looks like different BIOSes intercepted different keys, and then could probably manipulate an agreed-upon piece of hardware to set the speed, while also having the option for a dedicated hardware Turbo Key.
It doesn't explain how the BIOSes dealt with other applications wanting to use those keys, though.
Similarly, there's this manual for an AMI BIOS system which says
The 386/32 has a connector for a hardware processor speed switch. If this has been connected to the front panel of your system you can use it to switch between the maximum processing speed (of ten referred to as "Turbo") and the secondary slower processing speed. Pushing the switch on the panel changes the speed. If the higher speed is in use and your front panel has the appropriate indicator light, the LED indicator will light up while the high-speed mode is in use.
The processing speed can also be changed using a keyboard command sequence. To use this feature do the following:
Hold down the <Ctrl> and <Alt> keys simultaneously and press:
a + (plus) for the high speed, or
a - (minus) for the low speed
This looks like a similar way to do that, so maybe there was some kind of unofficial standard?
The Commodore PC10 III manual linked in the other answer is also very interesting, because it contains the full schematics of the motherboard, and the chip responsible to generate the CPU clock (among other things) is a Faraday FE2010A, so we have a description how changing the CPU speed worked:
The Configuration Register (I/O Address 0x63) is a write only register that is used for FE2010A configuration. [...]
Data Bit Function
[...]
5 Fast Mode (0 RAM wait states)
6 7.15 MHz CPU clock
7 9.54 MHz CPU clock
Which means it should be possible to write a TSR with any kind of hotkeys to change speed, as long as this information for the respective motherboard is known.