Support basic integration with a const IntegratorBase

[RussTedrake]

Moving this discussion from slack.

#22601 is pushing on something that I've been meaning to push for some time: allowing a LeafSystem to use an IntegratorBase integrator, without that integrator holding undeclared state.

Currently even the simplest apis for integration are non-const -- the IntegratorBase uses member variables for state in at least a few different ways:

1. it holds a reference to a mutable Context which it updates with the integration results,
2. storage related to error control / variable step integration,
3. book-keeping statistics (e.g. how many times the calc methods have been called),
4. scratch memory to avoid allocation inside the main integration loops.

But if we want to use an integrator to implement integration inside a system or constraint, then this corresponds to hidden state.

After a quick experiment here, my proposal is to offer a new entry point: IntegratorBase<T>::IntegrateWithSingleFixedStepToTime(const T& t_target, Context<T>* context) const which:

1. updates the mutable context argument,
2. doesn't need error control / variable step integration,
3. disable book-keeping,
4. still writes to scratch memory -- but these will be marked mutable.

We could consider more sweeping support for const integration APIs (e.g. the multiple step variants), but this is already a good start.

[RussTedrake]

@sherm1 -- do you prefer marking the book-keeping statistics mutable, or disabling book-keeping in the new const variants of the methods?

[sherm1]

My preference would be to make the stats always mutable and continue updating them in the const variants.