If you post a picture of the battery and a picture of the phone without its back cover, someone might be able to identify it.
For the difference between Birch and Chestnut, just turn off the phone and plug in the phone to charge it. Do you see a red charging light or not?
I think checking it in this way should work provided that the software installed on it is for the correct batch. Probably it could be misleading in case someone reflashed it specifying the wrong batch, but if it was never reflashed, or if whoever reflashed it did so specifying the correct batch, then I think this should work. If it says “librem5-r2” then you will still not know if it is Birch or Chestnut.
Edit: found a nicer way: look for “Machine model” in the output from sudo journalctl:
@Skalman That will work, but only assuming that someone has flashed the correct OS for the batch. You can have that mismatched.
Batches aren’t hard to identify visually:
is the rear camera’s flash positioned diagonally (top-left) to the camera? If yes, it’s either Birch or Chestnut; otherwise (flash next to cam on the right side) it’s either Dogwood or Evergreen
alternatively, where is the notification LED? If it’s on the left side, it’s either Birch or Chestnut; if it’s on the right side, it’s either Dogwood or Evergreen
If it’s either Birch or Chestnut:
plug it in to charge and turn the phone off. Does the red LED turn off as well? If yes, that’s Birch. If the red LED stays on while it’s charging when off, it’s Chestnut. (afterwards, push the power button for about 3 secs to boot it back up to verify that it was off - with some old software these batches could lock up with screen off instead of actually turning off)
If it’s either Dogwood or Evergreen:
take the back cover off. If there are markings that indicate where SIM/SD cards go etc. it’s Evergreen. If there are none - just some smooth plastic - it’s Dogwood.
alternatively, look at this photo - if it seems like the space under the screen is larger on the photo than on your device, you have a Dogwood. If it’s looks right, it’s Evergreen.
People have posted photos of the Birch, Chestnut, Dogwood and Evergreen batteries, and they have the number of mAh printed on the battery, so it is weird that your phone doesn’t. You must have a collector’s item.
Birch is the same as Chestnut, and Dogwood as Evergreen in this regard.
Birch, Chestnut and some (most?) Dogwoods.
Indeed, there’s also smart card reader placement, volume buttons being separate buttons or a single rocker, headphone jack placement, probably some more things I’m forgetting about and we haven’t even touched functional differences