Only items that increase your AGI and therefore increase your taxable income potentially affect your tax bracket, items that are not federally taxable income do not. Roth conversions are taxed as ordinary income. If your intent is to stay in the 10% bracket for 2023 for the Single filing status and under age 65, that means keeping the total of your income taxable as ordinary income below $24,850 ($11,000 plus the standard deduction of $13,850) and your total taxable income, including that which is taxed as long-term capital gains, below $44,625, above which long-term capital gains start to be taxed at 15% instead of 0%.
These sorts of what-if calculations are most easily done using the CD/download version of TurboTax. You can increase the amount that you report for Roth conversions incrementally and see where the increment in tax liability is greater than 10%. For example, you can increase the amount of a Roth conversion $1,000 at a time and see where the corresponding increase in tax liability becomes more than $100.
You might also want to take state taxes into account if you might jump between state income tax brackets.
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