How do I disable double-vibration when I dock my iPhone?

Short of disabling all vibrations (General > Accessibility > Vibration) in Settings, there is no way to accomplish this when running stock iOS, at least AFAIK.

The question linked below appears to be identical and has some suggestions, none of which are perfect answers (they all have downsides):

Turn off buzz when plugging in iPhone

If you're just trying to avoid the buzz at specific times (your partner or child is asleep nearby), then that page missed one (which I can't add because I don't have sufficient reputation):

https://osxdaily.com/2017/04/24/silently-charge-iphone-ipad-no-sound-buzz/

tl;dr - if you have the camera open already then the device won't vibrate when you connect it to power. Even if your phone is locked, you can usually access the camera from the Control Center (unless you've disabled that).

I've tried this with my iPhone 6S on iOS 13.7 and this works as of 5 Oct 2020.