Pianists are trained to play the thumb from their abductors and ironically the thumb's weakest muscle is its abductor. They are also trained to cross the thumb under the palm but there too, the flexor intersects with the long flexor of the index finger and that both grinds the two tendons together and locks up the extensors.
The best and most efficient way to play the thumb, especially if you have an injury is to combine three movements. The first is not a movement per se but, play down using the weight of the arm. No thenar muscle required. The second is to use the pronator to play down. Combined with gravity this gives the thumb true effortlessness. Using the pronator this way is often called "forearm rotation." Like the way you would play trills or tremolos, play the thumb from the elbow. The third is playing forward into the keys. THIS IS NOT PRESSING. It is just playing forward. Combine the three and the thumb muscles are barely used.
There are several movements which get in the way of the thumb such as radial or ulnar deviation, dangling it, extending it, hyper-extending its phalanx, not moving in/out . . . I did them all!
Our fingers are not designed to play flat and by default, the thumb is flat, and sideways. It is designed for flexing and gripping, not abducting. The way around this is forward shifting but careful not to twist the wrist.
There is no such thing as relaxation at the piano. Muscles must be engaged somewhere. The question is, which ones? Often we use the wrong ones to play and relax the correct ones. We get too focused on the fingers and not the arms where all the muscles that actually move our fingers are located. Our fingers for the most part have no muscle. They are moved via pulleys called tendons which are activated in the forearm.
Sometimes it is not what we are doing right but what we are doing wrong that causes problems. A single errant movement such as abducting can counter everything good. I am a firm believer that proper movement promotes healing. I had bilateral tendonitis from building a deck on the back of my house and for two years I was in great pain. My last six months I was totally paralyzed and couldn't lift a fork, brush my teeth, pull on a sock . . . I even drove my car from my knees. No doctor could help. I finally found a woman who opined that I had to re-learn how to move. After working with her for one hour, I didn't even realize it but she asked how my hands and arms felt and for the first time - I had no pain. Now, I wasn't healed but this was the beginning of my healing.
Google Edna Golandsky and find out if she has a student/teacher near you. She is in NYC.
The body is a machine with levers, pulleys, rubber bands and fulcrums. Playing the piano requires a knowledge of physics and biology. Most teachers just know about matching notes and that is not sufficient. They only know what they were taught themselves and it is what they DON'T know that can hurt their students.
EDNA HAS A WEBPAGE. Who knew? Nobody knew this before (My Donald Trump impersonation). https://www2.golandskyinstitute.org/teachers/find-a-teacher