@Paul ******
Not at all. You do not have to pay taxes in a state you do not live in. That is true if you move from one state to another in the US. You only pay where you are a tax resident. You may be a tax resident in two states during the first year transition or if you maintain a business, property, or certain other ties to your previous state. There are tax residency criteria but if you don't meet those criteria and no longer live in the state then you don't pay taxes there. That is true if you move abroad as well. I do pay federal taxes and I vote by mail through my previous CA voting office.
Earlier this year I got a letter from the CA Franchise Tax Board saying that they noticed that I didn't file a tax return in 2019, my first year of not filing CA taxes. They said I owed $6,000. I sent them a copy of my passport showing that I hadn't been in the US more than a couple of weeks for the past 4 years. I also sent them copies of my Thai drivers license and Thai government pink ID card. They responded that I was no longer a tax resident and could disregard the earlier notice. (Note - they sent the notice to my address in rural Thailand)