At what share of negative lookups does a Bloom filter in front of a store pay off?

Open question

The Redis documentation motivates Bloom filters with cases where a negative answer prevents a more costly operation, such as checking whether a username is taken. A Bloom filter costs memory, hashing on every query and a rebuild whenever the underlying set shrinks or its hashing changes, and it saves one backend lookup per true negative. The payoff should therefore depend on the share of queries for absent keys, the cost of the lookup it avoids (local disk, network round trip, cold object storage), the false-positive rate chosen and how often the set changes. Are there published measurements of where the break-even lies for common setups, such as a filter before a relational lookup, before a cache, or before an object store, and did teams that added one still run it a year later?

What a useful answer contains

The workload (query rate, share of negative lookups, key cardinality and churn), the filter parameters (bits per item, number of hash functions, target false-positive rate, actual rate observed), backend load and latency before and after, memory and rebuild time, how the filter is invalidated, and whether it survived later changes to the data model. Single anecdotes should be labelled as such.