feat: integrate callback saving into integrator init and finalize

Author: AayushSabharwal

lib/OrdinaryDiffEqCore/src/integrators/integrator_utils.jl

@@ -240,6 +240,7 @@ function solution_endpoint_match_cur_integrator!(integrator)
             copyat_or_push!(integrator.sol.alg_choice, integrator.saveiter,
                 integrator.cache.current)
         end
+        SciMLBase.save_discretes!(integrator, integrator.opts.callback; skip_duplicates = true)
     end
 end
 

lib/OrdinaryDiffEqCore/src/solve.jl

@@ -574,6 +574,7 @@ function SciMLBase.__init(
         end
 
         initialize_callbacks!(integrator, initialize_save)
+        SciMLBase.save_discretes!(integrator, integrator.opts.callback; skip_duplicates = true)
         initialize!(integrator, integrator.cache)
 
         if _alg isa OrdinaryDiffEqCompositeAlgorithm