You don't need to buy that puck, it's not the issue - at least not the way you think.
The motor IS the actuator, the black plastic puck is a housing for the cables that actually do the work. They are wrapped around a spindle / pulley that has a gear cast into the plastic, and the motor turns a worm gear that rotates the pulley to pull on the cables.
For the seat locks, the cables retract the locks (which is why the handle ALSO pulls them up to move the seat) and the issue is that the motor / cables are still pulled tight and that's why the seat won't lock into place right now. If you can see from your image, there is a plastic arrowhead clip (upper left of your image) that is holding the plastic puck to the seat. There's a couple of these IIRC. Push them aside and you can remove the puck by sliding it out from the metal clip. Then you can unscrew it and open it up - and you will see how to release the motor from it and rotate it to release the tension. At that point the whole thing SHOULD be functional again, at least manually.
I disabled the motors in my seats (unplugged) to prevent any further shenanigans from Darth Elon's programming and ridiculous design.