2004 Lincoln Aviator P0305 and P0316 Codes After Using 87 Octane Gas

I recently purchased a 2004 Lincoln Aviator. The previous owner had the vehicle smogged that same morning, and it passed successfully. However, shortly after, the engine began idling roughly. About 24 hours later, the Check Engine Light (CEL) activated. I scanned the codes and initially found P0420. Realizing I had just added 87 octane gasoline—when the vehicle requires 91 octane—I suspected fuel quality might be the issue. The next morning, the CEL was flashing, indicating a misfire. To address this, I used an octane booster, drove for a short distance to circulate the fuel, and then refilled with 91 octane gasoline. After re-scanning, the P0420 code disappeared, but new codes appeared: P0305 and P0310. The vehicle still runs fine overall, but the idle is rough and inconsistent. It's highly unusual that a vehicle passed smog inspection just hours before experiencing these issues. Could the low-octane fuel have triggered or caused these misfire codes? I'm seeking confirmation on whether this scenario is plausible or if there could be another underlying mechanical issue.