Is it permissible to combine the Dhuhr and Asr prayers after the Asr prayer time has begun due to time constraints at school, bearing in mind that the questioner regularly observes the Rawatib (supererogatory prayers) and performs them later?

It is not permissible to intentionally delay the Dhuhr prayer to pray it with Asr; for delaying a prayer beyond its time and combining two prayers without a valid excuse is among the major sins. You must be diligent in performing the Dhuhr prayer within its time. If you are unable to do so and are harmed by abandoning your studies, then it is hoped that you have a dispensation to delay Dhuhr until the time of Asr, with the intention of combining them as a delayed combination (jam‘ ta’kheer).

If you pray Dhuhr without its supererogatory (ratibah) prayers due to time constraints, it is prescribed to make up those supererogatory prayers, and it is preferable to make them up before the Asr prayer.