A few things that may help others:
- Where the guide suggests using a PH 000 screwdriver, I found more success in using a PH 00.
- Reconnecting the battery requires pushing the battery connector down quite hard. The white connector should sit almost flush with the black port; if the white connector is quite raised still then it won't be connected and your switch won't charge or turn on.
- If the switch shows a Nintendo logo before immediately turning off, and the switch fails to charge, you likely haven't pushed the battery connector down fully.
- You can test that the battery is properly connected immediately after connecting the battery connector by turning the switch on. You do not need to reassemble the switch or reconnect the SD card port first.