The other is https://wordpress.stackexchange.com/questions/259181/receive-a-custom-parameter-with-rest-api
I think the question "How do I add a custom parameter to core REST routes/controllers" is solid - and that it's at the heart of what they're asking. But the author's been inactive for a few years, and I feel like I'd need to replace just about everything they have written in order to improve it's quality and create congruity with the answer I have in mind...