Hooked it up to powerbank, through my USB power meter
it's hard to see, but it's reporting 0.45 watts power consumption. I programmed it to do a bit more wifi traffic, and this didn't really change.
I soldered a JST connector onto the solder pads on the back of the board labelled + and -. Unfortunately, my standard polarity meant the connector is over top of two of the pins.
I'm conforming to Sparkfun and Adafruit's standards for these connectors. I also put a blob of Weldbond on top of the pads, hoping I won't rip them off connecting and disconnecting the battery.
It didn't work off this battery alone. I plugged in USB power, and the battery charge LED which was flickering before is solid. After 5 minutes, it's now working off the battery alone. The battery must have been dead.
Charging, the USB power meter now shows 1.0 watts power consumption. I gifted some of these
https://www.amazon.ca/Soshine-6w-Performance-Monocrystalline-Cellphonefor Christmas a couple of years ago. I should borrow one!