Is following the funeral procession interrupted by performing the post-prayer Sunnah or by attending to a need and then catching up with it before burial, and what is the criterion for following?

Following a funeral is a right of a Muslim upon another Muslim, and it entails great reward. This full reward is attained by accompanying the funeral procession from the time it leaves the deceased's home until burial, based on the Prophet's (peace be upon him) saying: "Whoever attends a funeral until the prayer is offered over it will have a qirat, and whoever attends it until it is buried will have two qirats." In another narration: "Whoever follows the funeral of a Muslim out of faith and seeking Allah’s reward, and remains with it until the prayer is offered over it and the burial is completed, he will return with a reward of two qirats, each qirat like Uhud. And whoever prays over it then returns before it is buried will return with one qirat." So, whoever falls short in this will not attain the full reward.