What should we add?

Right now the UnitarySynthesis 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

One aspect in particular is there are a few synthesis methofs in the default plugin that are still implemented in Python: quantum shannon decomposition and xx decomposer. Of the two the quantum shannon decomposition is more important to have in rust because it's needed to synthesize unitaries for >2 qubits. The xx decomposer we should still port to rust but it's usage is much less common so but we can make sure to have a path that avoids calling it from c.

Pre-requisites:

• Oxidize ParameterExpression #13267 (for testing)
• Move source of truth for QuantumCircuit classical variables and stretches to Rust in CircuitData #14299