Let me expand on things a bit. I'll write some about the "technical requirements" as well as a bit about the "practical requirements".

The technical: I think it's been pretty well beaten to death over the years that code requires the shower pan has to contain water to a depth of 2" over the drain. So if you have a 2" vertical difference between the start of the sloped floor at the shower entry or threshold and the end of the sloped floor at the drain, you're good. With the 2" requirement satisfied, the entire "bathroom" floor can be flat and the floor only needs to slope within the "shower" footprint itself.

Water has surface tension, and as such it can move to areas not within the shower flood plain due to capillary action. So it makes sense to add a capillary break under the tile at the threshold to prevent water from being wicked from the wet area within the shower to the dry area in the bathroom.

Technically, you only need waterproofing within the shower and you only need an impervious material like tile on the floor within the shower's flood plain. On a practical note, it makes sense to include both a capillary break at or near the threshold and to extend the tile (or an impervious flooring material) as well as the under-floor waterproofing to an area a few feet outside of the shower.

Those few feet of protection outside of the shower will protect the floor from shower over-spray and provide a protected "drying off area", etc.

With all that written, your question was "Is tile the only flooring option?"

Inside the shower and for practical purposes the few feet outside the shower, you want a material that won't be damaged by water. That material is typically a properly rated tile or an appropriate natural stone. Man-made materials can also suffice.

Once (technically) outside the shower flood plain and (practically) a few feet away from the shower entry and on the bathroom floor, you can use whatever material you like on the remainder of the bathroom floor. Wood, cork, tile, stone, etc.

I've done a few curbless showers in that fashion: Tile or stone in the shower and extending a couple of feet out in front of the shower entry, then another flooring material (wood, cork, a different type/style of porcelain or stone tile) on the remainder fo the bathroom floor.

You specifically asked about soapstone. I've fabricated shower pans from solid soapstone slabs. I've tiled shower pans and tiled bathroom floors in soapstone. Soapstone itself is a fine choice for a shower or any other wet area.

For a remodel, yes, floor stiffness can be a concern, especially with a natural stone floor. The floor can be structurally stiffened, and membranes can also be used to decouple or isolate the tile from floor movement.