Both of those would be red flags for me, even though my current awesome T does do relaxation and meditation with clients. He actually recently told me he did not feel that those would be appropriate right now given my heavy struggles. Therapist pull the “don’t worry be happy” crap with me at this point and I literally just up and walk out, they can send a bill if they want paid. I spent three months actively looking for my current T after three years of passive looking. What helped me the most was taking an honest inventory of the traits of the most healing people that have been a part of my life (friends, teachers, clergy, therapists, authors... anyone).
I had looked at current T before but wasn’t too keen on his favorite types of therapy (a lot of group crap and experiential), he was a man and I am not too comfortable with men in general, he works and lives in a higher income kinda stuck up area, he was too damn happy in the picture... just no, nah, nope and YUCK! But... after I wrote down stuff about all the really influential healers and support people in my life I was brought full circle back to him and knew I couldn’t call anyone else. It took me a month to email him and I could not call to save my life... but... he is TOTALLY awesome with me.
I knew I was in the right place when he did things like stand a little farther away when coming to the waiting room but then read my body language and approached to shake my hand. He let me know he never wanted me to feel pressured to tell him anything before I was ready and still asked some deep questions and never shied away from anything. He asked me what I was looking for both in therapy and with a therapist and was honest (and accurate) about his areas of strength and weaknesses in being what I needed.

Red flags I should have picked up on with previous therapists that didn’t work out...
Reassuring/comforting me without understanding the issue and not allowing space to work on it rather than just comfort.
Not being clear about their expectations from a client, changing expectations or having low expectations.
Following what the book said you should do rather than trusting their skills/intuition and what they saw from me
Too eager to prove they knew how to work with me/someone like me.