It's taken me a long time (two years) to feel that she does....
But I feel that she cares in a professional, boundaried, limited way, and that's good!
She shows me she cares by...holding strong boundaries, asking me to trust her with difficult stuff and showing me that I can, remembering stuff just when I need her to, being calm, kind, and predictable.
I can email her between sessions if something is bad or if we've had a difficult session she says I can email her. Which I like, but I don't necessarily think that's a sign of caring or not. Just different approaches/boundaries/contracts/time!