I noticed that leaves/logs don't have the tags "minecraft:leaves" or "minecraft:logs". Since they're not meant to be obtainable even via silk touch they shouldn't need it I suppose, but I'm guessing it's part of the reason they're not harvestable. No Tree Punching doesn't realize that they're leaf blocks and therefore it's not a block you're allowed to punch to harvest.

I tried adding the leaves tag via crafttweaker to see if it would fix it, but apparently not.

Attached are some screenshots displaying the issue.

1. This is entirely possible within No Tree Punching's set of configuration features for block breaking. The reason leaves are always breakable is because they're added to the always_breakable and always_drops tags. See the wiki for details.
2. In this case, NTP should just reference the leaves tag for future mod compatibility.