Bent Wood

Normal plywood is very rigid because the grain direction of each layer alternates within it, therefore it won't bend after it's manufactured.

You can get "bendy ply" and then glue/laminate several layers of it into any reasonable shape, but you'll need plenty of clamps and asuitable former ...

get some insulation foam - high density underfloor - and carve a former using saws, wire brush and sanding paper

cover it with clingfilm stretched tight, and then use several layers of heavy glass cloth and polyester resin to make a fibreglass armresty

Or buy a chair that is the right shape?

Agreed. Though I did once impress my late father-in-law (master builder, and amazing carpenter) by bending 1.5 metres of skirting board to fit a curved chimney breast (about 40 cm iirc) by putting it inside a vertical length of cement-asbestos drain pipe with a steam cleaner hose into the bottom for about half an hour. You would probably get away with ABS soil pipe too.

You would probably need to make it rather than get it.

For bending you have two options really. The traditional; make up a clamping form in the shape you want, get some veneers, glue up and odd number with the grain oriented in alternate directions, clamp em to the former and let them set (vacuum clamping is good for small items like this), and leave it to set before trimming to final size.

Or, kerf bend a bit of ply; make multiple, parallel, close spaced non thorough saw cuts in one side of the ply in the area of the bend, so you leave a thin section un-cut. The ply should now bend to shape with the saw cuts on the inside of the bend. To make the bend permanent, fill the kerfs with a gap filling adhesive like epoxy, bend to shape and leave for the glue to set, then sand clean.

DUI Make it.

I've seen those usually made of some stuff called formwood, which I think is a plastic that looks like it has a grain. Brian

You can't. There are many other ways to do it.

taste so bad it has form

Alternatively don't bend anything, cut the curves and stack multiple layers similar to this?