I just uploaded a version of this that is thinner, and makes the AirTag case back visible on the outside.
First Version of a holder - this is shared more as a reference design than a final product. You can use it as-is, but it needs some refinement. Pocket is a bit large, and the thickness can probably be reduced a bit.
Unfortunately, after adding this to the remote the remote is no longer quite as loseable, somewhat defeating the purpose of the AirTag.