I've seen over a dozen therapists. Only three were a good fit long term.
At first it was stressful when one didn't work out, but as I've healed more, I felt more of a sense of agency and the ability to decide to move on without it being a bad thing. Every therapist is unique. Working with many over my lifetime has taught me a lot. Even ones that I saw for a relatively short time taught me something.
It sounds like you are finding your empowerment, and you value your time and money and health. It sounds like you know what you need and want and just need to trust yourself and take the stressful action of termination of this therapeutic relationship so that you can find someone who is a better fit. Therapists are service providers and if you don't like the way one does things, there are dozens of others to choose from usually. Fit is everything and if you're not feeling it, definitely move on.
I get the EMDR thing. I was told I am not a candidate for EMDR due to my Dissociative Experiences Scale score and level of symptoms. My nervous system was not in a good place for it. I had the EMDR therapist for a while and she taught me grounding and resourcing and similar techniques. But it wasn't meant to be a long term talk therapy relationship, and I am still not safe for EMDR. I moved on and do not wish to pursue it.
I know myself well enough to say EMDR is not a good idea for me and may never be. And so I focus on working with therapists who are not fixated on that modality. I don't know why, but there are many therapists who are really super into very specific modalities that are not going to work for everyone. From Internal Family Systems to EMDR to tapping to brain scans, I've seen it all. I speculate that some therapists like the structure provided by these modalities as it helps them to focus and feel secure and confident and know what to do. It takes a really special person to be able to do pure talk therapy and keep all the boundaries and have it be therapeutic and incorporate CBT etc. But they are out there! I would leave this person and look for a new one. It might even be something they can help you with if you bring it up.
Chances are if the rapport is sinking, they feel it too and may be relieved to help you find someone who can provide what you need.