One thing I thought I noticed was that the brake pedal felt hard when I went to engage the gear select.
I have now confirmed that that IS a relevant symptom.
Since all the 12V stuff was working as normal, I revisited the HV connection.
I disconnected and then re-connected the HV isolator.
When I tried things again - after that - it was fixed.
That HV isolator looks and feels like it came from the $2 shop. Very fragile and dodgy.
I have read on here somewhere (or on a link from here) that if the "isolation level" of your i3 is above 14-03-504 then "it is not necessary to deactivate the high-voltage system". Given the flakeyness of the HV isolator, I would heed that advice in the future.
So. Going again. Very relieved.