Bad fuel economy/shaking low rough idle?

This is going to be detailed. I’m having this problem where when I’m at very low speeds but mostly stopped at like a light (not in park), my RPMs go down to 500. My car then kind of does tremble or shake. It’s not super aggressive, but a passenger even can feel it a little bit. However, then my RPMs will go back to 1000 and then kind of repeat that process until I drive. It’s kind of inconsistent. Sometimes it does it, other times not so much. Sometimes it’s a little shake, other times it’s more aggressive. I am also getting poor fuel economy. I’m not sure what my car specifically gets, but it’s getting 20 mpg on the dash. A question was, “Well, maybe the dash is wrong.” But honestly, I can tell my gas mileage is bad. I have to fuel weekly to a full tank when all I do is go 5 miles to work and back, so I don’t think it’s wrong. Those are the symptoms. Only those two. With that being said, when I first got the car (2 months ago), I cleaned the battery with a baking soda and water solution. The next day, a check engine light came on code P0607 indicating an ECM problem. I cleared the code because I thought it was just because of me cleaning the battery. The code is yet to come back on. I was doing research on what could be causing these problems because my car isn’t misfiring. I’m not stalling. Acceleration seems fine. Everything seems normal except for those two symptoms (poor gas mileage, rough shaky idle). Since then, I have cleaned the throttle body, cleaned the MAF sensor, checked for vacuum leaks, and checked the engine filter. And it has been none of those, and I just can’t seem to figure out the problem. And I’m not sure if someone could even help me, but if anyone has any knowledge that could help me, that’s greatly appreciated.