For the benefit of other people who haven't been in a serious building fire: what were your other options?

Windows.

Every building is different, so my advice might not be useful for you. I'd recommend researching your building and figuring out several escape strategies, including the details like how you will protect yourself from the smoke (smoke will be EVERYWHERE, and you really don't want to breathe it in). If a fire is something you're worried about, I'd recommend writing/printing out your escape plan and posting it somewhere, e.g. in your closet, because there's a good chance you will be too scared to remember it when the time comes.

Based on my experience, my one very general piece of advice that everyone should take into account is this: figure out if there are any "single points of failure" in your escape plans. That is, is there a single location where a fire could start that would block ALL your escape routes? In my case, the fire was on a first floor apartment across the hall from the elevator, between the two staircases, and also directly below my apartment's fire escape, so this single fire blocked all 4 of my easy escape routes. If you identify such a situation, think about what you will do if a fire does start there.

All that said, here are some things I could have done, which I came up with after the fact. Obviously I haven't tested any of these, so take them with a grain of salt:

Break into someone else's apartment and use their fire escape on another side of the building.

Find a way up to the roof and walk across to the other side of the building, which has its own separate hallway with 2 staircases and an elevator. Alternatively, I could have tried to break through my bedroom wall into the adjacent unit, which connects to the other side hallway.

If it came to it, I probably could have got my quilt soaking wet in the bathtub, draped it over top of my body for protection, held my breath, and sprinted down the stairs and out of the building. It turned out that while the smoke was going up both staircases, the fire was limited to only a single apartment unit, although of course I didn't know this at the time.

Outdoors, the fire was only blocking the staircase side of the fire escape. I could have descended down the other side of the fire escape by hanging down off the side and dropping down to the floor below me, one floor at a time, and then jumping down to the ground.

I have a long rope in my closet that I could have tied to my radiator and let out my bedroom window on the other side of the building. This would have been quite risky, because there's a lot of unknowns: How much weight can the radiator hold? How much can the rope hold? Am I strong enough to support my weight with my arms on a rope?

Lastly, it turns out you're unlikely to die from jumping out a 4th story window. (International note: 4th story is 3 floors up from the ground level floor) You're not terribly likely to walk away from it either, but a broken leg is better than dying in a fire.

How? The staircases are usually located at opposite sides of the building. The entire first floor would need to have been on fire.

There is one exit on the first floor, between the two staircases. The apartment on fire was the closest one to this common exit, directly between the two staircases and across the hall from the elevator, so the smoke went up both staircases equally.

At least here in Germany that's the default. Fire and smoke will absolutely not spread between (fire-)units. Staying put is absolutely fine, obviously if you can get out that's encouraged but with a single set of stairs staying put isn't a death sentence at all.

If the building is properly compartmentalized, you're supposed to stay in your apartment in case of a fire (unless yours is the one that's on fire, obviously!)

This is a pre-war building, so I have no idea what the fire code was like when it was built. That said, this fire was indeed contained to only the apartment where it started and I think one or two adjacent apartments.