Yes, if your income was earned evenly throughout the year then you should use the number of months of residence divided by the full year to arrive at the percentage for each state.
You should also prorate your unearned income. If you believe it was relatively even in 2021 you can use the same formula. If not, you can look at your quarterly (or monthly) statements to see actual earnings for each residency period.
As far as the IRA, when you go through the state returns there may be an ability to enter the deduction for each state, otherwise, depending on the state rules for each state there may be a calculation of taxable income against total federal taxable income after adjustments to income (IRA deduction). Each state has their own way of calculating the part year resident taxable income.
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