I went through something similar but different. Was in counselling with a low-fee agency and the counsellor advised that I needed to see her more frequently. Before I was seeing her fortnightly or three-weekly in order to space out the allocated sessions and that worked well for me.
As soon as I started seeing her weekly and our work intensified, she behaved oddly. She cancelled sessions without notice saying that she had taken on other (child protection) duties. I was angry because I didn't want to see her weekly and work more intensely and since she had suggested it, I thought it was irresponsible to then not be available for it. It sent the message that my deeper pain wasn't important.

Then, a month or two further on, I learned that she had been sick. Not serious, but some stomach disorder keeping her awake at night. She took time off sick and all my sessions were terminated.

I suppose that in some situations where a counsellor/ therapist has been so-called "unprofessional" towards a client, then it's embarrassing for the agency and the supervisor to come clean. But I still think it should happen.

Since then I've never gone back to low fee counselling. I feel that if there is an administrative, political, personal situation affecting an agency counsellor's ability to continue in her work - then the supervisor should sit down with the counsellor and client and talk openly and respectfully about the situation.

There is something weird about agencies that purport to "help" and then get in a muddle and can't talk honestly about it. Honesty always feels more respectful to me.

In a situation where a counsellor has done something construed as "unprofessional" towards a client, I can see that it would be difficult, embarrassing or legally dubious for a supervisor to come clean about it - but I still think it should be done as a healing of trust. Admitting what you have done badly, etc.

I don't understand your agency dealing with you in this way. Can you write to them and challenge it?