I'd like to be able to use an existing NEMA 14-50 to power some power tools that are designed to run on 240 volt, 20 amp plugs. To prevent serious damage to myself or any equipment (e.g., table saw gets jammed), I'd like to build something (maybe an extension cord, even if it's not particularly portable) to limit the current draw to 20 amps, while still maintaining 240 volts. I understand how the 50 amp plug is wired, so I'm good there, but is there a reasonable way to essentially build a portable breaker box that plugs into the 50 amp outlet? I feel like this would be a pretty common thing, but I haven't been able to locate anything prebuilt, so feel free to let me know if this is a really stupid idea.
You can buy such a box off the shelf, or build one. It's a plug-in sub-panel aka a power distribution box. The better class use breakers.
Note that this is only the case because you have a 14-50 outlet. A 10-50 outlet would not be acceptable. By the time you get all the parts together a pre-built unit may be the better deal. But if all you really need is a couple of outlets, build-your-own may be a win.
You need a suitable range cord (or other suitable cord and plug) for inlet, a sub-panel and suitable cord clamp for the input cord, GFCI breaker(s) for the sub-circuit(s), and (for practicality in building your own) metal surface-mount boxes with exposed-work covers for the appropriate receptacles for the sub-circuits, attached either to the sub-panel box or all attached to a mounting board or box of some sort. If you have 120V circuits you can use a regular breaker and a GFCI outlet (usually costs less) for those. I have not seen (but might exist) GFCI outlets for 240V receptacles.
Sounds like you are not planning to use this outdoors, but since that's a common application scenario for "construction power" someone doing that wants to choose parts suitable for outdoor use if that is the case - weatherproof boxes and in-use outlet covers.