2016 Mazda 3 i touring 2.0L

80k miles, automatic

Symptoms:

• CEL (p013a, p0171)
• (occasional lurching/throbbing?) vibration when idle and at low speeds
• vibrations worse on cold start
• 3-4 times the engine wouldn't start within minutes after shutting down (silent, no sputter)
• needing to refuel twice in a 5 day work week traveling ~75 miles from half a tank

Maybe symptoms:

• stiff pedal until start
• sucking noise

There were a couple times the brake pedal was stiff and I had to press it hard to get the car to start, this happened a week or two ago. I've had the vibrations for almost half a year so far, and it seems to take a week for the CEL to light after clearing. I took it back to the dealer and all they did was replace an O2 sensor and clear the codes, after which I took it to a mechanic who wanted to replace the left and right mounts and see what codes come back after clearing. Took it to another mechanic who said there was nothing wrong with the mounts as the engine didn't have too much play, no clunking, and that it might be the spark plugs. I replaced those but that doesn't seem to be it. I have also noticed a sucking sound a couple times recently but that could've been background noise far as I know. I haven't read any additional trouble codes, and the mechanics haven't found any others.

Might this be an ignition problem and should I look at the coils next, or could it be vacuum related and what should I pay more attention to in order to determine that? Could one problem cause it all?