Add storage locations and methods for classical variables to QuantumCircuit

[jakelishman]

Add the new public-API methods and internal tracking to QuantumCircuit necessary to handle the new manual variables as described by Qiskit/RFCs#50.

Copied from the RFC, the new public API surface looks like:

class QuantumCircuit:
    def __init__(
        self,
        ...,  # existing structure
        *,
        inputs: Iterable[expr.Var] = (),
        captures: Iterable[expr.Var] = (),
        declarations: Mapping[expr.Var, expr.Expr] | Iterable[Tuple[expr.Var, expr.Expr]] = (),
    ): ...

    def add_var(self, name_or_var: str | expr.Var, / initial: expr.Expr) -> expr.Var: ...
    def add_capture(self, *vars: expr.Var): ...
    @overload
    def add_input(self, name_or_var: str, type: types.Type, /) -> expr.Var: ...
    @overload
    def add_input(self, name_or_var: expr.Var, /) -> expr.Var: ...

    def store(self, location: expr.Expr, value: expr.Expr, /): ...

    @overload
    def get_var[T](self, name: str, *, default=T) -> Union[expr.Var, T]: ...
    @overload
    def get_var(self, name: str, *, default=NotGiven) -> expr.Var: ...
    def has_var(self, var: Union[str | expr.Var]) -> bool: ...

    # All variables, including inputs and captures.
    def iter_vars(self) -> Iterable[expr.Var]: ...

    # All do what they say on the tin.
    def iter_declared_vars(self) -> Iterable[expr.Var]: ...
    def iter_input_vars(self) -> Iterable[expr.Var]: ...
    def iter_captured_vars(self) -> Iterable[expr.Var]: ...

[jakelishman]

Closed by #10974.