In general, ankle braces are made to protect the ligaments of the ankle, not the tendons.
As such, ankle braces are generally made to protect against abnormal side to side or twisting motion.
The ligaments hold the bones together, so they don't move side to side or twist past one another abnormally.
The ligaments on the other hand go from the muscles to the foot bones to control movement, not to provide any strength at the ankle level. Indeed, the tendons are made to glide freely at the ankle level:
To "rest" the tendons, an ankle brace would have to significantly restrict ankle movement so the tendon isn't being flexed/extended.
But any ankle brace that restriced flexion/extension would make playing tennis difficult.