Bifoldable Laws with non-commutative types

I noticed that the existing bifoldable laws for Binested fail if you use Tuple2 instead of Either as the two-slot type constructor, and a non-commutative monoid for the innermost types. e.g. adding

checkAll(
  "Binested[Tuple2, ListWrapper, ListWrapper, *, *]",
  BitraverseTests[Binested[Tuple2, ListWrapper, ListWrapper, *, *]]
    .bitraverse[Option, Int, Int, String, String, String, String]
)

fails cats.tests.BinestedSuite.Binested[Tuple2, ListWrapper, ListWrapper, *, *]: bitraverse.bifoldRight consistent with bifoldMap, vs the existing one, which passes:

https://github.com/typelevel/cats/blob/b036fb47196d1a788db09eb2bc262071fa3cb928/tests/shared/src/test/scala/cats/tests/BinestedSuite.scala#L86-L90

Assuming the implementation is correct and the failure hasn't revealed a bug, it makes me wonder if there's a way to encode this in the types. Should the C: Monoid on BitraverseTests.bitraverse be C: CommutativeMonoid so that the law is more universal? If so, how far up the chain should that propagate? Ultimately it's used in BifoldableLaws.bifoldLeftConsistentWithBifoldMap and BifoldableLaws.bifoldRightConsistentWithBifoldMap.

Start with the Binested law check in tests/shared/src/test/scala/cats/tests/BinestedSuite.scala and the C bound in laws/src/main/scala/cats/laws/discipline/BitraverseTests.scala. Run the Tuple2/non-commutative example, then trace BifoldableLaws.bifoldLeftConsistentWithBifoldMap and bifoldRightConsistentWithBifoldMap. Done means the law's required algebraic typeclass and its propagation are agreed and consistently represented in the tests and laws.