(Java 1.16.2)Is there a way to detect a pulling bow and play sounds via resources packs or commands?

Solution 1:

The only sound in vanilla minecraft that occurs when pulling a form of bow is when loading crossbows, not standard bows.

Those sounds are as follows:

item/crossbow/loading_start
item/crossbow/loading_middle1
item/crossbow/loading_middle2
item/crossbow/loading_middle3
item/crossbow/loading_middle4
item/crossbow/loading_end

and you can find the wiki page on them here and here.

If you want to make standard bows do this, you'll probably need to mod the game.