How does gift tax/capital gains tax work with real estate? (Specific situation)

I have an particular situation I need some answers to. My ex and I lived together for 3 years in a house that was in my name. They gave me money for a down payment as well as spent some of their trust fund on things for the house and upkeep, I payed the mortgage for the entirety of the time. I just sold the house and I'm splitting the profit with them, but we're both wondering about how capital gains tax and gift tax might factor in.

I know that since I lived in the house and didn't run business out of it, I'm not subject to capital gains. Will my ex have to pay it since the house wasn't in their name?

Conversely, will I have to pay gift tax since I'm giving them more than $14k?

We can prove that we both had money invested in the property and both lived in it for at least 2 years of the last 4. Will that be enough to prevent these taxes on our profit?

Thanks Reddit! I wish I knew a CPA personally, but...I don't.