I'm not a native speaker but I think they describe a different situation or attitude: "I sat" implies a more active actitud or purpose than "I was sitting". While I was sitting would merely reflect a passive position," I sat" in this case describes the fact that the person has sat down for a particular purpose (in this case to eat the cake).
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AnonymousIf I had not read it from an authentic source I would have thought it had a grammatical mistake, and would've corrected it into (was still sitting). The question is: why is it correct as it is?It is fine. The past simple or past progressive is a writer's choice.
Anonymouswould've corrected it into (was still sitting).It's correct as it stands, but I, too, would have chosen "was still sitting". I believe it sounds more literary with "sat", and the author, too, might have said "was still sitting" in an ordinary conversation.