I had just asked the developer of Unclutter (which I’ve used for years) about this issue. The relevant part reads “…if the extension doesn’t provide these special flags, Unclutter will not recognize this data as sensitive.”
WHY doesn’t BW provide whatever these flags are? The whole point of BW is to protect passwords, so if it CAN use a flag to indicate to clipboard apps not to show passwords then it obviously SHOULD. I’m not getting the issue.