The Pico[1] is pretty much the RP2040 on a breakout board, and is breadboard mountable (also includes the necessary usb interface).

[1]https://www.raspberrypi.org/products/raspberry-pi-pico/

Just solder pins to it and plug it in to a breadboard.

It is kind of a bummer that it seems to be 0.1" wider than a DIP socket.

What prevents you from using the Raspberry Pi Pico for that?