Muji sells a travel soap container that has a large cell sponge inside to prevent it from getting too slimy
PP Soap Dish with Lid L L size. I've also seen a smaller one in some of the stores.
I've traveled with my own toiletries for quite some time. Some are decanted into hotel mini-bottles and honestly, I haven't come across much hotel product in the last few years which I've wanted to take home. A good bottle is more likely to appeal. I look for a flip top, stands on cap (gravity feed), and thin/flat so it doesn't take up much space in 3-1-1 shape.
Most of the hotel products use licensed brands and are distributed by the same suppliers
https://www.flyertalk.com/forum/24908454-post9.html I'm one of the weird people who reads ingredient labels and I doubt that the hotel versions use the same formulations as the retail versions. They have a variety of water conditions to deal with, wider variety of hair & skin to satisfy, cost significantly less than the brand's retail product, and most of the good "expensive stuff" have equally long ingredient lists which don't fit on the small bottles in 1 sq inch. That's fine if you like a product for the scent or branding but not that useful if you want a specific retail formulation or to avoid some common low-cost ingredients due to sensitivity.