Love this question because not many people ask this.
For me, it depends on how invested I am in the story. If it's something short and fun, then I can move on quickly afterward because the plot was straightforward and the end was happy and satisfying. I savor it, but not for a long time, I like to think of what I enjoyed about it, whether I would recommend it, and then move on.

I tend to linger on stories that I have invested a lot of time reading or watching. Stories that have high stakes drama and keep me on the edge of my seat. Or those dark, psychological thrillers, that make you question humanity. Where characters aren't always so likable but feel real with hard decisions to make, and sometimes I don't like the outcome but I can understand why it happened. I really savor things like that, because it's easier to make something happy or to make something flow with cliched events that aren't pushing the envelope (and nothing is wrong with that). But for those writers who do, they want their audience to think on a deeper level and I try my best to answer them. Being a writer myself, I understand.

So all in all, I do enjoy savoring the things I have read. Whether it's a short read or something longer, both can teach you many things and bring forth ideas and perspectives that you might not have thought of before.