Update PauliString.__mul__ and __rmul__ to handle GateOperations

Enhanced PauliString multiplication methods to handle GateOperations
that can be interpreted as Pauli strings (e.g. X**2) by using the
existing _try_interpret_as_pauli_string function.

Addressed part of #7588, for the PauliString * GateOperation cases, e.g. `x*x*x**2`

Author: ToastCheng

cirq-core/cirq/ops/pauli_string.py

@@ -271,6 +271,8 @@ def __mul__(self, other):
             known = True
         elif isinstance(other, (PauliString, numbers.Number)):
             known = True
+        elif (as_pauli_string := _try_interpret_as_pauli_string(other)) is not None:
+            return self * as_pauli_string
         if known:
             return PauliString(
                 cast(PAULI_STRING_LIKE, other),
@@ -297,6 +299,8 @@ def __rmul__(self, other) -> PauliString:
 
         if isinstance(other, raw_types.Operation) and isinstance(other.gate, identity.IdentityGate):
             return self  # pragma: no cover
+        elif (as_pauli_string := _try_interpret_as_pauli_string(other)) is not None:
+            return as_pauli_string * self
 
         # Note: PauliString case handled by __mul__.
         return NotImplemented