The first of the stuff from eBay arrived today.

The Lolin 32 (I actually think it's a Lolin 32 Lite) arrived:

I plugged it into a USB port on my hackinosh, and the LED on 22 flashed. :)

I had to download Arduino IDE again (rebuilt hackintosh since last programming stuff). Also followed the instructions to install the ESP32 capability. Of course, it didn't show up in the IDE under the Tools->Ports. After a big of google-fu and head scratching, I remembered that when I ordered some clone Arduino nanos (some time ago) I had to install some drivers. Inspecting the board (you can see a 16 pin chip bottom left) it says CH340G and this matches the link I found last time. I installed the drivers, selected Board: Wemos Lolin 32, Flash: 80Mhz, Upload speed: 921600, Port: /dev/cu.wchusbserial1410.

I got the example "Blink" sketch. Hit compile & upload and it completed. Except nothing flashed.

Then I realised that the standard sketch assumes a standard Arduino and the pin with the LED is 22 on the board above. So I changed that and it worked!

Also checked the WiFi scan sketch and that worked too.

When the batteries arrived, I tested one of the 18650 Li-ion cells at 3.8V. Having disconnected the USB, I tried plugging it into the holder and touching the wires to the battery leads on the board, and that worked too.