Does my deceased mother's house count as inherited if I am listed on deed with rights of survivorship and how will the profits on the sale of the house be taxed?

My mother purchased a primary residence home for herself in 2018 for $200k.

When she was diagnosed with terminal cancer in February 2022, she added my sister and me to the property deed as joint tenants with rights of survivorship (we never lived there, let us assume that the property was worth $280k in February 2022). She passed away in June 2022 (let us assume that the property was worth $290k in June 2022) and we are selling the house for $300k in August 2022.

How will the profits on the sale of the inherited house be taxed?

  1. taxable as long-term capital gains on full appreciation from the purchase price in 2018 ($300k - $200k = $100k LT capital gains)
  2. taxable as short-term capital gains on the appreciation from the time that we were added to the deed? ($300k - $280k = $20k ST capital gains)
  3. taxable as short-term capital gains on the appreciation from the time that my mother passed away? ($300k - $290k = $10k ST capital gains)
  4. untaxed because of the six-month "alternate date valuation" rule (I.R.C. § 2032(a)(1))?
  5. something else?

If the answer is #2 or #3, do we simply do our best to estimate the value of the house at the time that we were either added to the deed or at the time that my mother passed away? or is there a more formal appraisal required?