Is delaying making up missed prayers without an excuse considered a reason for apostasy (kufr), or does the ruling of apostasy for abandoning prayer apply only to current prayers and not to missed ones?

As long as you have repented to Allah for abandoning prayer, you are not considered a disbeliever. Disbelief due to abandoning prayer is related to the present prayer, not those that have been made up.

Since you are afflicted with obsessive whispers (waswasa), you have leeway to adopt the view of those who do not obligate making up prayers for someone who intentionally abandoned them, as one suffering from waswasa is permitted to choose the easiest opinions.

If you wish to make up the prayers, then do so according to your ability, in a way that does not harm your body or livelihood.