I went through this a year ago with the therapist I was seeing at the time. The big difference was the change in jobs was sudden for me. But if I were you I'd try juggling things out with her first especially if you haven't already started the new job. Once you get a feel for the schedule and work you may find a way to work it out. Like that maybe your boss is willing to work with you so that you can leave early, or come in late if you can balance it by coming in early or staying late on another day to balance the work or some kind of set up.

I was probably more upset and internalizing a lot of the blame at the time, though I know she must have either felt guilty or something because she asked about me being upset with her even. We'd tried phone sessions and her assistant tried to help, but my new schedule was even worse and fluctuated way more than they initially implied. There had also been some scheduling mishaps for the first time since I'd been seeing her. Like her assistant would call if there was an opening, I'd accept, then it'd get canceled without a call to reschedule/confirm l had always received in the past. This left me feeling worse and zoned in on my always a burden feelings and that I'm unwanted, etc.
I think looking back, I try to keep in mind that I don't really know what was going on on the other end. That it's unlikely that she reassured me while also thinking there's a big chance that this might not work out in my favor. It's more likely she doubted the chance that my new job schedule would be inflexible that we'd have to stop. If I recall I think she even offered to write a doctor's note saying I'd had a standing appointment, but being new I knew this would result in me not keeping fulltime status and losing hours aka income that I couldn't afford to miss out on. But yeah this a sucky situation and during the transition to a new job can be extremely overwhelming, I hope you find something that works for you though.