I am wondering what is the etiquette of publishing a "folklore" result?

Though special cases of the result are well-known, the proof is not readily available in any reference text or paper I've seen. I will include it in the background of my thesis, and I could stick it onto another paper which I am working on (in which I use the folklore result). However, the paper I am working on is in a very niche area, whereas the proof of this result is useful to the bulk of researchers in my field.

My options are:

Include it in my current paper, which is in a niche subfield

Put the result into a (very) short paper and submit it to some journal

Post the proof on arXiv, and not submit it to a journal

Post the theorem and proof on nLab

What are your thoughts? Are there any journals that accept this sort of "folklore" publication? Or am I better off just sticking the proof in my current paper or posting the proof on arXiv or nLab?