In reply to Ella Morris:
Soft shell is kind of a broad concept. When you say climbing, what kind of scenario? Are you thinking rock/multi-pitch/mountain rock? Or snow/ice/alpine too?
Some soft shells have a degree of insulating property, like an inner fleece etc. but originally I think they were intended more like a tough and somewhat breathable outer layer - one to wear over a base layer (if conditions are warmer) or over mid layers (if colder), and then you still have the option to put a hard shell or belay jacket on over the top.
Not quite sure about what might count as 'canvassy' but for a decent robust soft shell without additional insulation there are things like this:
https://www.mountain-equipment.co.uk/collections/womens-soft-shell/products... (lighter)
https://www.mountain-equipment.co.uk/collections/womens-soft-shell/products... (mid weight)
Or for ones that are more protective and/or warmer:
https://www.mountain-equipment.co.uk/collections/womens-soft-shell/products... (looks light but warm)
https://www.mountain-equipment.co.uk/collections/womens-soft-shell/products... (this is basically bombproof but maybe not as breathable and will probably run hot depending on conditions).
I've linked to Mountain Equipment as I like their stuff and somewhat know their range (no affiliation though) but Rab, Montane, Patagonia etc. will all have equivalents.