I had the blinking purple/pink light when fully charged. It turned out to be a battery balance error. it would go away after the bike was ridden for awhile so the battery level dropped. The bike would only operate in level 1 assist until the error went away. However, a firmware update on the bike at the Dealer fixed it. It turned out to be one of a few bikes that had a firmware bug.
Not saying this is your issue, because I do not have the extender, but if the bike was not getting fully charged and an extender was plugged in it would get a full charge from the extender after awhile. Or it could just be a mis-balanced battery in the main battery or the extender.
Usually in a Lithium ION battery there are 2 or more banks of batteries to get the 250 watts of battery power are achieved. These different banks are charged separately at the same time and sometimes one bank charges faster than another so the charger will vary the current of charging to each bank until they all arrive at the same voltage and then charging is complete. This takes longer than a straight charge, but it keeps a stronger bank from overcharging while the weaker bank comes up to voltage.
Take it to the dealer and they should have the update device that will plug into your bike to update the firmware. They also have the Dealer app that lets them inspect errors that do not show properly on the ebikemotion app.