This bug is relevant only for CQF/bonsai. Since the ABT translation layer relies on FieldPath (e.g. here), the restrictions on field names are different than the existing find/agg systems.

As an example, the following query should work:

assert.commandWorked(coll.insert({a: {$b: 1}}));
assert.eq(1, coll.find({"a.$b": 1}).itcount());

But instead throws with ""FieldPath field names may not start with '$'. Consider using $getField or $setField."

At least two relevant JS tests are field_name_empty.js and field_name_validation.js.