Yes, you are close, the 0% rate for long-term capital gains is valid for singles with taxable income of up to $47,025 in 2024 ($48,350 in 2025). If your income, including the capital gain is in the 0% bracket, there is no capital gain tax.
You may also be able to exclude the gain on the sale of your home if you lived in it for 2 out of the last 5 years before the sale. A single person can exclude $250,000 under this rule. See: See: Qualifying for the exclusion
