I have steep stairs leading to the basement. the washer and dryer

I had the same problem in a 100-year-old house. I had a trap door/laundry chute that got the clothes down there and then up again via the chute. I used a laundry bag as the laundry basket and made sure it was small enough for the opening.

Up until we put in the chute, I used an old-fashioned clothesline where I could pulley clothes up and down without navigating the stairs with a basket. https://www.vermontcountrystore.com/searchresults?Ntt=clothesline%20pulley&Nty=1&No=0&Nrpp=12&Rdm=665&searchType=simple&type=search

Again, I went with laundry bags to haul up and bring down. (I actually threw most clothes down, but the pulley helped me haul everything back up.

There are some new laundry baskets- I saw them at Walmart. You can carry them with one hand, as they flex inward to form a handle.

I bump the basket up one stir at a time. It takes slightly longer than carrying it, but is easier and no chance of losing my balance. I also bump them down, by backing down the steps and having the basket a stair above me. This way I don't have to lift the basket very high and I lean on the basket for balance so no railing needed. If steps are no too far apart I can bump two steps at a time.

In a laundry basket.

I too have steep steps to my basement and laundry and I use the flexible mesh laundry baskets to take my clothes up and down. I keep a regular basket in the basement to transfer my clothes from the washer to the dryer and just use the flexible one to carry my clothes up and down. They have two sizes, a small one and a large one that has dividers in it for up to 3 small loads. Works really well for me and I feel safe carrying my clothes up and down. I also make sure my phone is in my pocket when I go down, just to be safe.

You might be able to build a pulley system. But the safest thing is to buy or build a tilted wagon so that the back wheels are on a lower step while the front wheels are on an upper step. Build a frame with netting and attach to the wagon base so you have a basket in which to pile or stack the dry clothes. If you fix a rope to the wall next to the staircase at the bottom and top, running it through the handle of the wagon first, you can pull the wagon up the staircase. The rope is your safety system. If you have to turn loose of the wagon handle suddenly, the worst that would happen is that the wagon would plummet back to the basement with your clothes still in the net. If you don't already have a railing BUILD ONE. Best wishes 😇💞

Get an extra large zippered gym bag and when it's full of dirty clothes just roll it down the stairs. When you come back up use a heavy cord to pull it up behind you. Or, with a longer cord, you can go all the way back up the stairs and then turn and pull up the bag. If you're young and agile maybe you could carry it up like a back pack..

I use those oblong baskets with a handle like you take to a picnic or carry casseroles in. They are so easy to carry up my stairs. They are light too and sell them at most chain stores. :Laundry baskets are too hard. always hitting my fingers on door jams and walls with that. I fold my clothes in basement and you would be surprised how much you can pack into those baskets. Have a laundry chute to send clothes down. Not big enough to use something to bring them up