

Checked and found that US citizens don’t have inherent right to work in EU - it’s only easier to travel, not to settle down.
And speaking of renting - it really depends. If we’re talking about Copenhagen, it is expensive, the market is broken (thanks AirBnb), and it’s really hard and expensive to move in. I burned through my savings and owed some money to my employer before I could invite the rest of my family into a freshly-rented apartment. But if we’re talking about “a bed under a roof”, it’s super easy to find a room on FB Marketplace, and live with a couple of other internationals.
So if it’s just about “getting out of US” (crazy, I never thought it would be a thing, I’m sorry for them), then finding work is a must, but in a big city you usually can find something. It’s only hard to find something nice and permanent
Denmark is fine for trans - nobody cares who you are, in a way that you have the same rights.