Does the current prayer of a worshipper—performed on time and in congregation—become invalid due to his failure to make up previous missed prayers (Fajr, Dhuhr, and Asr) that were intentionally left, knowing that ترتیب (observing the correct order) is obligatory?

One who intentionally abandons prayer has committed a grave sin, and their repentance is not valid unless they perform the prayers and cease abandoning them. The prayers you have performed are valid, and there is no requirement for a specific order between missed prayers and performed prayers, or between different missed prayers, although it is recommended. You must make up the prayers you have missed, along with repenting to Allah, and you must abandon obsessive thoughts and not succumb to them.