I think I have figured out what is wrong. The replacement Energizer battery has a stepped edge, meaning the positive face of the battery does not extend fully down the height of the cylinder. The positive terminal in the sensor is roughly where the the positive terminal of the Energizer battery ends and the negative terminal begins, and so it is not fully in contact with it (and possibly is shorting the two terminals on the battery).
A picture should help. The (original, works) Lixing battery is on the left, the (replacement, does not work) Energizer is on the right:
So I just need to find a battery that is shaped like the Lixing (a constant diameter cylinder) rather than the Energizer (two cylinders of different diameters).
I have no idea whose fault this is - Energizer’s or Lixing’s (one of them didn’t follow the standard, or maybe there isn’t a standard), or SmartThings for not designing the sensor to accept either implementation of the standard.
And I don’t think a shim is going to work.