That would be correct, but give a look at this model that may work for you.
https://www.opticsplanet.com/franklin-armory-5550-binary-trigger-gen-3-22lr-9mm-metal.html
After going to link and reading all descriptions and specs, clearly states “will not function in polymer lower…”, the S&W M&P 15-22 only manufactured with Polymer lower.
Couldn't you just buy a standard AR-15 binary trigger?
Correct, this trigger is made specifically for the Ruger 10/22 platform. Your best bet for finding a binary trigger that will work for that is going to be a Fostech Echo-II, and you'll have to get Fostech's .22 sear trip for it to work with the .22lr. It is unfortunately a very expensive setup, and frankly, probably not worth the cost if all you plan to shoot is .22, as the setup will end up running you the same as the complete rifle you mentioned.