Yesterday, on December 5th, the Switch was updated to version 4.1.0. This message was included in the patch notes: “Resolved an issue that caused motion controls to respond incorrectly when playing games that use the feature.”
After testing it today, I found that the gyro bug I mentioned above was indeed fixed. I did not experience it once today. Before the update, it would occur almost every single time I started Splatoon 2. It would only stop after resynching the controllers or recalibrating the gyro sensors.
For anyone who regularly plays games with gyro aiming on the Nintendo Switch, this is certainly cause to celebrate. The update may not have included highly requested new features such as a web browser, but it is certainly a welcomed bug fix.