If I hit a throwable with a bat with infinity, a copy of that item gets added back into my inventory. You can't pick up the thrown version. I assume this is the intended way it should work.

However if I hit that same throwable a second time, I can pick it back up, duping it.

version: webasemod-1.18.2-1.3.1.jar
forge: 40.1.73

Ah, this (bugged) mechanic is still a remnant of the previous way of throwing up throwables to hit with bats.
Now that throwing a throwable up is done by using a bat, it is much simpler to scrap this previous behavior altogether and just ensure that throwables are not reduced when using a bat with infinity.