And no where in there does it say she quit being a Republican and ran as an independent.
She ran as a write-in, Republican candidate. Alaska law at the time allowed that for write-in candidates to still claim a party even without being the nominee. The list of write-in candidates that could be requested at the time even listed her as a Republican.
Well I can’t say that’s wrong since I wasn’t there. But that would be very unusual, and she certainly was not the GOP nominee.