I’m strongly leaning towards a new perspective. As other have said it can give more depth to the world by showing us sides of it we haven’t seen before. Before continuing a story that already had a satisfactory ending, I think you should think very carefully about whether the installment adds to the story or detracts from it. Not knowing when to let a finished story stay finished is how sequelitis happens.
In general, I’m quite skeptical when it comes to doing sequels to interactive stories. Unless the story was planned out in advance to have multiple installments, what usually happens is one of two things: Either the sequel picks one ending of the original to be the “canon” ending and thereby invalidates the playthroughs of anyone who didn’t pick that path. Alternatively they somehow try to obfuscate the ending of the original, coming up with a series of events that would plausibly set the stage for the sequel regardless of which ending the player got in the original, thereby running the risk of invalidating the playthroughs of all players regardless of which ending they got.
The greatest feature, in my opinion, of interactive fiction over traditional fiction is the feeling of agency, the feeling that the player is part of the story and can affect things around them. Nothing kills that feeling like a sequel that shows that none of the decisions you made previously actually made a difference at all.
Having a previous PC return as an NPC is tricky for a similar, but more intimate reason. When playing the player will tend to come up with an idea about who their character is and why they are doing what they do. If their old character then shows up as an NPC, especially if you let them interact with them, you run the risk of going against the player’s own interpretation of that character. As the author you are free to tell a player that their interpretation of one of your characters is wrong (well, some people disagree on that, but that’s a separate debate). The player however usually perceives the PC as more of their character than yours, and telling them that their interpretation of their own character is wrong doesn’t sit well. “My MC would not have done that.”
In conclusion, I’m not saying you shouldn’t write a sequel to an interactive story, I’m just saying you should be careful so that you don’t end up making the players feel as if they are just an observer watching through a character’s eyes instead of an actual part of the story with the ability to affect the world around them. In general I think that’s easier when you make potential “sequels” rely as little as possible on the events of the original story.