I don't have an official source, but both TurdoTax and TaxSlayer seem to indicate that portion is not taxable.

HOWEVER, that could be based on old information from the tax-free state Covid help (Alaska also has the energy rebate in 2022, which qualified to be tax-free).

https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/enter-alaska-energy-relief-p...

https://support.taxslayerpro.com/hc/en-us/articles/8772996566042-Alaska-Permanent-Fund-Dividend-Taxa...