The lounge of Jack and Jill's villa at New Hampstead. The essential furniture consists of a table, on whcih are writing materials, and two chairs. As the curtain rises the lounge is empty, but Jack and Jill come in immediately, followed by Aunt Jane.
Could you explain me why the comma (the pink coloured) has been used here?
I'll start with the second "pink" comma. It is there to separate "immediately" from "followed" because the author does not want you to think "immediately followed".
The first "pink" comma is not required according to some writers, but is there to improve the readability. One issue is that the tone of the voice rises at "empty" and the comma imitates the intonation. Another thing that sometimes happens if you habitually don't separate "but" from a preceding clause is confusion with what the conjunction is intended to coordinate: "The person responsible was not the butler summoned but the plumber who was already there believed it was." This last sentence needs a comma before "but".
There should also be a comma between "rises" and "the lounge". Because the adverb phrase occurs before the subject of the main clause, the comma is needed to signal that the main clause begins with "the lounge". Otherwise a person may (temporarily) imagine that the adverb clause says "the curtain rises the lounge".
The implication of the commas in the preceding sentence (about the table and chairs) is that a table is part of the essential furniture with or without the writing materials, but the writing materials are also present on the table. Without the commas, the implication would be that the table requires the writing materials (and the two chairs) for it to be essential as well as that the chairs are on the table with the writing materials.