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Removing the existing behavior will almost certainly not be accepted, because of backwards compatibility.
Adding new functionality is generally acceptable.
Doing that through a new keyword that defaults to the old behavior is fairly common, and generally better than an apparently redundant function. But in this particular case, that makes the new signature and documentation such a mess that I believe a separate function would be the lesser of evils. (And that only if it is clear what the problems with the current situation are. e.g., do the problems only trigger when using the database from too many threads, or is a random network delay enough to trigger problems?)