It turns out picking that threshold is extremely difficult - I've tried! The value seems to differ for different searches, so picking eg 0.7 as a fixed value isn't actually as useful as you would expect.
Agreed that thresholds don't work when applied to the cosine similarity of embeddings. But I have found that the similarity score returned by high-quality rerankers, especially Cohere, are consistent and meaningful enough that using a threshold works well there.
I'll add to what the other commenter noted, but sometimes the difference between results get very granular (i.e. .65789 vs .65788) so deciding on where that threshold should be is little trickier.
Why not have a similarity threshold? Say, if the distance is below 0.7, do not accept the search result.