Typing into ESP8266 with a USB keyboard
My 2002-era Mac keyboard doesn't work, 


That doesn't surprise me - modern Macs have never needed PS/2 support.


  none of my 5 wireless keyboards work, 


That's because they're not keyboards, they're wireless transceivers that provide USB HID interfaces.


  and neither do Xbox or foldable keyboards. 


Too modern, and of course XBox has never needed PS/2 support.


  Nothing that presents as a composite device works (like a keyboard with USB slots), only dead-simple (no fancy keys/knobs) keyboards seem to work.


Of course, they aren't PS/2 keyboards, they're USB devices.

Older keyboards provided dual operation - USB and PS/2. This is a function provided by the keyboard, not the USB standard. Mac keyboards, since the Apple computers never had PS/2 ports (since PS/2 is an IBM standard from the PS/2 computers back in the 80s &amp; 90s). Modern keyboards that provide more than just a simple keyboard functionality cannot really provide PS/2 as well since that can't provide the other features of the keyboard. The same goes for composite devices, or wireless devices - they facilities they provide are in excess of what PS/2 can provide, so it would be illogical trying to provide PS/2 support - especially as PS/2 ports are getting rarer on computers now.


  Would a USB host module (like the Uno shield, but not a shield) let me read from more than just basic PS2-emulating USB keyboards?


Sure, if you can get the libraries working on the ESP8266, which may well be a huge challenge in- and of itself.


  Is the code to read basic alphanumeric keys consistent among different keyboards, or will each model need special instructions? (much like a driver would provide an actual OS)


All USB keyboards are class-compliant HID devices. They send HID reports in a standard format, maybe with custom additions. The basics are always the same though.


  If it's anything but "plug and play", what would be a simple way (no soldering) to securely input passwords into an MCU?


It'd be far from "plug and play" getting a USB host interface working with the ESP8266.  Consider other more simple routes, such as using serial, or configuring the ESP8266 as an access point and using a web browser to configure it.