Sorry this gets really complicated because you don't give some key details.
(1)
You owe state taxes if you are domiciled in a state. Your domicile is your permanent residence. There is no single factor that controls, but important factors include your main home, location of professional relationships (doctor, lawyer, etc), social relationships (church, clubs, etc.), driver license, voter registration, car registration, and so on. To leave a domicile, you must take active steps to abandon the prior domicile, like ending a lease or selling property, and establishing a new domicile elsewhere. It is possible to be temporarily away from your domicile for a long time -- years even -- without changing your domicile. While I don't know all the facts, it seems from your limited details that you are not domiciled in any specific state for 2024, so you don't owe state taxes unless one of the exceptions below applies to you.
(2)
However, there are 6 states that can tax you if you work remotely for a company located in that state. They generally use a "convenience of the employer" test. That means that if you work overseas because your company asked you to, you are not taxed in the state. But if you could work in-state (they have an office you could use and they would be happy for you to work on site), and choose for your own convenience to work out of state, the state is still entitled to tax you.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/form-w-2/employer-withholding-state-taxe...
The exact implementation of the rule varies from state to state. For example, New York can't tax you if you work remotely and never set foot in the state during the year. But if you spend even one day in New York, the state can tax your entire income if you are working abroad for your own convenience. You will need to check the rules for the specific state if you live in one of these states.
(3)
You seem to be a W-2 employee? So this may not matter. But California has a slightly different rule for self-employed (independent contractors, 1099-NEC). California does not tax W-2 wages if you live out of the state, but if you are self-employed, California taxes you based on where your customers or clients are located, not where you are located. So if you are a 1099 independent contractor and some of your clients are in California, California wants to tax that portion of your income.
(4)
Also, you also owe state income tax if you perform work while temporarily living or working in a state. For example, if you visited the US for 2 weeks, and you continued to "work from home" while staying in a hotel or visiting family, the state where you are staying can tax you as a non-resident (in this example, they would tax 2/52nds of your income). This is difficult to enforce and relies a lot on the honor system, so you might get away with not reporting it, that's up to you.
(5)
Note that if you have state withholding on your US W-2, you need to file a return for that state to report zero taxable income and get a refund of the withholding. The state may ask you to prove you are not a resident. You can contact your employer to stop your state withholding if you are not a domiciled resident of any state and not subject to the convenience of the employer rule.
(6)
Lastly, if you are present in the foreign country for at least 330 days a year, you may be eligible for the foreign earned income exclusion on your federal tax return. This means that income earned from working is only taxed in the country where you live and work and not in the US. Unearned income (like investment income, pension, and so on) is still taxed in the US.
https://www.irs.gov/individuals/international-taxpayers/foreign-earned-income-exclusion
(7)
And of course, if there is a tax treaty between the US and the country where you are living, you may be able to claim a credit on your US tax return for foreign taxes paid on the same income.
