Yes, I’ve taken it in for repair. But they didn’t find anything because the restarting and popping sounds stopped happening exactly the day I handed it over.
Warranty covers any repairs but I ended up paying about $40 as you aren’t covered if they can’t find anything. The restarting and popping sounds aren’t recorded or logged by the iPhone in any way so you really have to be “lucky” that the bugs occur while the technician is looking at the phone.
It should be noted that there are no Apple Stores in my area so I was forced to take it in to an Apple certified repair shop. I don’t know if Apple would have charged that fee.
But like you said, these bugs are definitely related to charging: It seems I can avoid the bugs entirely if I only charge wirelessly. So that’s what I do mostly and only occasionally do a cabled fast charge if I’m in a hurry.
Since doing this I don’t seem to experience the bugs. But only time will tell if this will last.