Vanilla MC 1.16 assigned the hoe as effective tool for a bunch of things including leaves.
Would make sense if Quark blossom leaves also had the hoe being the effective tool, guess with this vanilla feature the axe being effective tool for leaves feature becomes a bit obsolete or weird to say the least.

Also noticed the blossom leaves don't seem to drop sticks at all, vanilla leaves have been doing that since 1.14, small detail but might be worth considering for consistency.

Sticks not dropping is intentional.