To what extent is the collective ختم (recitation leading to completion) of the Qur'an permissible online, whereby each member reads a portion of it in their home with the intention of a collective ختم?

There is no basis in the Sunnah or the actions of the righteous predecessors for the collective ختم (completion) of the Quran in the manner described. Rather, it is known that each of them would recite the entire Quran and supplicate for themselves, their families, and the believers.

It has been reported from the predecessors that at the completion of every recitation, there is a supplication that is answered. Therefore, if a person supplicates after completing the recitation for himself, his parents, his teachers, and other believers, this is permissible.

Mujahid, 'Abdah ibn Qatadah, and a group of people would display their Mus-hafs (copies of the Quran), and when they intended to complete a recitation, they would invite people to attend because mercy descends upon the completion of the Quran.

Anas ibn Malik, when he completed the Quran, would gather his children and family and supplicate for them.

Therefore, a Muslim should recite the entire Quran himself and supplicate for himself and for the believers, following the example of the righteous predecessors.