I wouldn't want my intervention to seem out of place, but shouldn't it be your teacher who suggests the way to solve the problem?
There are certainly exercises, but they depend on the type of problem encountered.
The path you must follow is to exploit gravitation and the weight of the arm. The shoulder must control the movement. The only thing that must be firm is the musculature of the hand, which must support, bear, and perform the function of discharging the weight onto the piano keyboard.
One would need to understand if the muscular tension arises from a posture problem, or from a lack of knowledge regarding weight technique, and also understand which muscles tend to stiffen. The piano is not played with muscles! A fortissimo chord must not come from the contraction of the latissimus dorsi, shoulder, triceps, and forearm at a muscular level; it is merely a transfer of energy—energy flows in the form of weight from the lower back and discharges onto the keyboard via the shoulder-arm-forearm-fingers bridge; the muscles do not intervene.
It must be the teacher who suggests the best technique to resolve tension problems which, in the long run, can cause very serious issues (tendinitis, which is nothing to joke about); certainly, a solution cannot be provided via a forum. I, like other teachers, would need to see you and understand where the problem originates in order to suggest the right path to follow. Furthermore, even in terms of sound, do you feel that you are giving the right colors to the piece? The sound obtained through muscular tension is an objectively ugly, metallic, and harsh sound; you will notice this when you play using weight.
Horowitz used to say that the most difficult thing to do on the piano is to make it sing.
You will understand this deeply when you are put on the right track.
The legitimate conclusions are yours... Forgive this unsolicited intervention, but sometimes it is better to be incisive between the lines, to trigger an alarm bell and provoke reflection on methods...