why does holding 'd' on startup initiate internet recovery rather than hardware test?
Just because you hold d doesn’t mean the signal is correct. Also, I wouldn’t put any effort into running home diagnostics. That only tests for things like “One of the four tires on your car is missing.”
My move for this symptom is to call Apple or chat with them online. Ask for them to send you a link to test your battery remotely while the OS is running. That will tell you far more. Also, if you can’t get the os running or erase, reinstall it from recovery, then you have larger issues than even getting diagnostics to run.
They will either fix your issue or offer a flat rate repair so you know how much worst case a repair will be.
In the end, you’re in the correct screen you need to decide how to move forward despite your wanting a quick diagnostic. You need to get to system information and have the battery specific diagnostics run by Apple at this point.