This answer cites the Ralbag as interpreting a (critical-to-the-question) vav prefix on a verb as "or". I've heard before that a vav prefix is not always "and" and can be "or" or even "but". Is there any grammatical rule by which we can tell when to read it which way, or do all the non-"and" readings always arise from judgments about what would make most sense to the interpreter? Do Chazal generally agree on how any given vav is translated, making it received tradition and there are no explicit rules?
Vav does not necessarily mean and or or. It is a conjunction and translated according to context. I translate most vav's as a "soft then"- a subsequent event where formal written English would not put a then, but in a conversation, one might say "so then I..."
Other possibilities: but (although, however), while, since, therefore.
Actually, it always means “and” (In fact, even within words, it has a sort of connective role between the meaning of the letters before and after it). It’s just that sometimes, to get the same point across in English or Modern Hebrew, we’d prefer to say “or”, or even “but”. Some translators account for this difference in language grammar, and some translate literally. Just know that Vav means “and”.
It should be noted that “and” is the nearest translation possible, but not completely accurate. Vav, at least in Biblical Hebrew, is more of a grammatical function. Similar to how “stones” effectively means “multiple stone” but “s” doesn’t literally mean “multiple,” so too ו connects to the word before it to form a phrase, but doesn’t literally mean “and”. Effectively, it does mean “and” no matter the context, but not as a separate entity.