Lots of advice here, some of it good, some of it questionable.
Two things I’ll amplify from other comments: there’s a reason your therapist missed. It’s could be anything from messing up in their calendar app to a pet or a family member being injured it passing unexpectedly. This falls into the “shit happens” category. You’re allowed to be angry, upset, disappointed, or any combination - your time was wasted. There are generally two outcomes - 1) the miss was unintentional or unavoidable or 2) the therapist is unreliable. Until you find out that it’s case 2, recognize that a couple of wasted hours - in the course of your life- is small potatoes (perspective).
Another is the concept of “agency”. There are things you can affect in your life, in your relationships, and in the world. There are things you cannot. Nobody can force you to allow yourself to ignore the latter. They will always get under your skin. However, if you find yourself dwelling on those items, try and take a step back and identify things in your life you control or which you can alter/adjust. Finding those areas where you have agency allows you to impart your will, to be a positive force in your life trajectory.
I won’t even begin to tell you this is easy. It is a process and a way of interacting. Here’s an example - recognize your disappointment with your therapist but take the initiative to reschedule. Taking it a step further, the day before your next meeting, confirm the appointment. It can be a text or email - simple, low contact. If you don’t get a response, escalate near the end if the work day (or first thing the morning of the appointment) with a call. These are things you can do to manage your therapist and your collective schedules. Most professionals (I am one fwiw) will not be offended in the least with good (but not excessive) communication. If they are, or if the therapist still flakes out on you - well, we’re back to case (2) above and you’re on the troublesome path of finding a new / another therapist. BUT - you’ve done all you can in your power to make this a success. Recognize your initiative as a positive, personal attribute you will continue to leverage in your life.
I wish you the best!
Refund request time, you mean, right?