I think you may be confusing two unrelated problems.
Electronic stability control has nothing to do with “sluggish acceleration,” at least in the cars I’m familiar with. Electronic stability control kicks in with selective braking when it senses maneuvers that may cause loss of control (e.g. slalom-type avoidance maneuvers). Usually cars with ESC come equipped with an “ESC Off” switch that allows you to turn the ESC off under rare conditions when you do want wheel slip, like when you get stuck in snow and need the wheels to be able to spin freely. The “ESC Off” light on the dash comes on to remind/notify you when you have pressed the “ESC Off” switch. It should not come on unless you press the “ESC Off” switch. Why it’s coming on randomly, I don’t know. However, even with the ESC off, you shouldn’t notice any difference in normal driving. You would only notice in an extreme avoidance maneuver that caused the car to spin out.
As for the “sluggish acceleration,” that sounds like a totally unrelated issue.