Coat can change shape willingly as an action
The statistics for the coats are available in the basic rules and are therefore freely available on DND Beyond (page 269 in SRD).
Listed under "Actions", the coat has the following capacity:
The couatl magically transforms into a humanoid or beast that has an index of challenge equal to or less than his own or returns to its true form. He resumes his real form if he dies. All the material that he wears or wears is absorbed or worn by the new form (the choice of necklace).
In a new form, the couatl retains its game stats and speaking ability, but its AC actions, movement modes, Strength, Dexterity, and others are replaced by those of the new form. , legendary actions, and hauntings) that the new form has but that it lacks. If the new form has a bite attack, the couatl can use its bite in this form.
This ability does not have a defined number of uses and is not a spell. Therefore, it is an "action" at will that the mantle can perform as often as desired (within the usual limits of one action per round of combat).