Newsflash: Capital Gains: Federal, State, and Local

Hey there! My grandmother and I are residents of NYC. She currently owns a home that she bought for $150k. She thinks she can sell it now (24 years later) for around 450k.She estimates that the closing costs at the time she bought it was 20k. She estimates she has put in 20k of upgrades into the home over the years.Her current regular income is around 30k per year.From my understanding, the way Capital Gains would be calculated in this scenario would be:Federal: 0 Capital Gains tax since her regular income is low enoughNY State: Taxed as income. The taxable amount is $40000 (450k sale – 150k initial price – 20k closing costs – 20k upgrades – 250k single exemption + 30k regular income). According to https://smartasset.com/taxes/new-york-tax-calculator#xxpZ4FNdIu the difference in New York State taxes (using 2023 numbers) would be only $550. On her normal 30k income, she would pay around $1045 in State Tax. Since this would be bumped up to $40k for this one year, the amount would be $1595.NYC Local: Also taxed as income. The taxable amount is $40000 (same as state). According to https://answerconnect.cch.com/document/jyc0109013e2c83c2542d/state/explanations/new-york-city/nyc-tax-rates-blended-nyc-tax-rates her normal local tax burden when earning $30000 is $1048.95. For this year, at an income of $40,000 her local tax burden would be $1430.85. The difference being $381.90.Therefore, her total “Capital Gains” tax burden as a result of selling this home would be $1976.90What I’m not sure of in my calculations:Does that $250,000 exemption on real estate Capital Gains apply to State and Local as well? If not, her tax bill will be much higher.I’m not 100% sure if State and Local give reductions based on closing costs or upgrades either.Is there a way to eliminate the tax burden entirely by using that $10,000 to loan me money to buy a house of my own?(The base numbers are all estimates, I just want to know if I calculated correctly)Thanks!