In Spanish verbs don't depend on prepositions as much as in English; it's more about collocations than specific prepositions associated to particular verbs.
Google translates mostly from what people feed it, so it inserted the preposition that most often goes with the whole phrase, I think.
I'm tempted to say they all are interchangeable, but I would prefer "con" for concrete things, like the essay or the work, than for more abstract ideas like "my situation".
- Me siento mejor con mi ensayo. = Me siento mejor con mi trabajo. -> The thing I made is what makes me feel better.
- Me siento mejor acerca de mi situación. = Me siento mejor sobre mi situación. -> "Acerca de" and "sobre" introduce the issue I have been dealing with, and my position about it. Another similar expression is "con respecto a". Some speakers might say "me siento mejor con respecto a mi situación".
You may also find "me siento mejor
en esta situación" -> I'm living better now that my situation has improved.