Add Automatic Differentiated Jacobians to Velocity-Implicit Euler Int…

…egrator, fourth PR of RobotLocomotion#12528 (RobotLocomotion#12967)

Add Automatic Differentiated Jacobians to Velocity-Implicit Euler Integrator, fourth PR of RobotLocomotion#12528

This commit:
1. Adds automatic differentiation as a velocity-Jacobian computation scheme for the velocity-implicit Euler integrator, by following the model of ImplicitIntegrator<T>::ComputeAutoDiffJacobian().
2. Refactors ComputeLOfY() based on the templated <U> IntegratorBase<T>::EvalTimeDerivatives() to enable this computation.
3. Fixes the tests so that they reset integrators between testing the different Jacobian computation schemes, to force Jacobian recomputations. Filed RobotLocomotion#13069 so that this will not be needed in the future.
4. Removes the boolean flags that skip tests that require AutoDiff'd Jacobians.

systems/analysis/test_utilities/discontinuous_spring_mass_damper_system.h

@@ -74,6 +74,9 @@ class DiscontinuousSpringMassDamperSystem final
 
     // Second element of the derivative is spring acceleration.
     (*derivatives)[1] = force / this->get_mass();
+
+    // Third element of the derivative is the energy added into the spring.
+    (*derivatives)[2] = this->CalcConservativePower(context);
   }
 
  private: