What is the ruling on delaying the re-performance of missed prayers that were completed without purity due to obsessive-compulsive disorder, and is it permissible to re-perform them in batches on the following day while performing the new day's prayers on time?

If you are certain that something has exited from you, and it is not a matter of obsessive doubt (waswasa), then there is no blame upon you for delaying the making up of missed prayers (qada') if making them up is difficult for you, especially since it is permissible for a person afflicted with obsessive doubt to adopt the easiest of opinions. As for the current prayer, it must be performed before its time expires.