The state you were physically in when you earned the income. It does not matter where your employer is headquartered. You owe income tax to the state you were in while you earned the income. See that link for info regarding out-of-state employers.
Texas has no income tax, so no income tax returns get filed there. 😉
You are a part-year resident of NJ and NY and NY, so you have 2 state returns (NY and NJ) to file in 2021. The link has instructions for filing part-year returns. You might think that part-year taxes are proportional to the amount of time spent in the state, but that's often not the case.
Most states divide the income earned in that state by the total annual income to come up with a percentage. That percentage is then applied to the state tax on the entire year's income—no matter where it was earned—to prorate the tax liability. TurboTax follows the rules for each state.
If you're a part-year resident of New York and want to enter different allocations for income earned inside or outside New York State, follow these instructions.
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