What should we add?

Clifford.from_circuit has a list of 1- and 2-qubit Cliffords that it knows how to handle via updating the tableau directly. https://github.com/Qiskit/qiskit-terra/blob/1fb00e628a73f960980648cf9c4db0dfecc936ca/qiskit/quantum_info/operators/symplectic/clifford_circuits.py#L331

This list currently doesn't include some Clifford gates from the standard library like ECR and iSwap. For iSwap, this is not a problem because it's .definition is all Clifford, but ECR is defined in terms of RZX and so can't be converted directly. This partially covered by #9475 but requires falling back to the matrix form to reconstruct the tableau.