XP bar not resetting to zero after a snowball is thrown

I am trying to use the xp bar as a shot reloader where it gives a player a snowball when it reaches 1 xp level. It then stops adding xp points until the player throws the snowball, after which it will be set back to 0 xp. After that, it will load until it reaches 1 xp and give the player another snowball. The command sequence I'm using is:

Command block 1, impulse, activated by redstone circuit:

xp add @p[level=0] 1 points

Command block 2, impulse, always active:

give @p[level=1] snowball

Command block 3, impulse, always active:

xp set @p[nbt={Inventory:[{id:"minecraft:snowball",Count:0b}]}] 0 level

It works until the player throws the snowball. Once the snowball is thrown the xp level won't be set back to zero, meaning the player can't get snowballs again.

You're testing for a stack size of 0. That can't ever happen. Change it to Count:1b.