What should we add?

Right now the GateDirection pass is written primarily in Rust but still has some dependency on Python. We need to have an implementation that doesn't rely on Python when being called from the C API and then add a standalone function to the C API as described in #14245

The same is true with the CheckGateDirection pass which in the present pass manager is used as a conditional on the execution of GateDirection. We don't necessarily need to expose check gate direction as a standalone function, but we'll need a path to execute it without python so the full path transpiler can use it internally.

Pre-requisites:

• Add rust representation of control flow op #13271
• Oxidize ParameterExpression #13267
• Move source of truth for QuantumCircuit classical variables and stretches to Rust in CircuitData #14299