Dynamical decoupling: Support pulling through the whole circuit with non-clifford moments (#6718)

* Support a new feature of adding dd.

Previously, we only insert dd for split Clifford pieces. While, one use
case is to insert into consecutive idle moments cross Clifford pieces.
We also support merging remaining Puali op of dd sequence into starting
/ ending single-qubit operations of each consecutive idle ops.

* Pull through all the way.

* Apply comments; simply the code a bit; Add comments.

* apply reviews

* import cirq -> import ops, ...

Author: babacry