I think a T has to be realistic. She can't promise to ALWAYS be there. Nobody knows what the future holds. It's a bit like a marriage, you can promise to always be together, but things can get complicated along the way.
I thought it was very smart that she mentioned this:
She did confirm this evening that she promises to be there as long as she can and if she can't for some reason she will give me as much notice as possible.
That's what I call realistic.
And apart from that, I'm a bit scared that the fact that that's 'all she can offer' is something we have to learn to live with.

I don't get attached this easily. So for me it's not a problem to give a therapist a bit of time to figure out whether or not I can trust him or her. Often, by the time I start to feel the connection, it's often clear that I can actually trust this T.
So maybe you can keep a 'safe distance' for a while and work with this therapist until you feel comfortable enough. Nothing wrong with that, I guess.