OK I’m too lazy to convert this into a proper blog post, but Proposition 0.4 here is something I needed recently, which others might find useful. Lemma 0.2 might also come in handy. Please ask in the comments if you’d like more details!
Update (Sept. 29). James Newton pointed out that it’s not actually clear how to fill in the details in the “proof” of Lemma 0.1.i. Therefore, the results in Lemmas 0.1 and 0.2 of the document linked above are currently unproved in the generality stated there. Fortunately, I was able to recover some weaker versions of Lemmas 0.1 and 0.2 which still suffice for the intended application to cohomology of Stein spaces. The corrected writeup is available here.