Double-sided board but with castellated edges? Are we supposed to pin the RP2040 and seal it under solder, or pin the LDO / voltage regulator and seal it under solder?

Its impressively small but I'm not sure if its a practical design.

Doubling the size and making it one-sided would be far more pragmatic. I have a feeling this isn't "really" meant to be a practical design as much as just an exercise in shrinking / miniaturization (which certainly has its benefits to exercise your PCB layout + assembly skills).

But yeah, if this were a 20mm x 10mm one-sided design... if only to make sure that all the hot components were on the same side of the board for proper thermals (and so that the "back" lies flat as you SMD it to a larger board)...