2013 - The property was put under title of my sister's LLC
Which means "you" did not own the home or have any legal ownership in it at all.
2021 - The property was given back to me as a gift (no monetary exchange at all); the property value is now expected to be ~$500k.
If you sell the home in 2021, you will not qualify for any type of capital gains exclusion at all. In order to qualify, the property must have been your *primary* residence for at least 2 of the last 5 years you owned it, counting back from the closing date of the sale. Since you did not own the home prior to 2021, and it was never your primary residence for any period of time after 2016, no part of the capital gains exclusion rules apply here. Additionally, if you sell the property within one year after you obtained title/ownership of the property, then you will pay the higher short term capital gains tax rate. If you own the property more than one year prior to the closing date on the sale, then you'll pay the lower long term capital gains tax rate.
Please consult with a professional in your local area to confirm all the above. But for the most part based on the limited information provided in your post and making no assumptions on my part, you just flat out do not qualify for any exclusions.
