Apple Pencil Pro on new iPad Pro repeating clicks & letters

My new 2024 13" iPad Pro with Apple Pencil Pro has slowly developed this problem:

—when I click on the screen, in Safari or in an app, with the Pencil, it often registers as a double click, which is most noticeable in those cases where clicking a 2nd time undoes the action of the 1st time

—when I'm typing by tapping with my Pencil on the screen keyboard, those taps also register double or even triple, giving me lots of words with repeated characters

My taps on the screen with the Pencil are always very light. And I don't have a tremor or other problem with my hand that would would cause my taps to repeat.

It's getting most annoying, because while the problem took a few weeks to worsen, now about every 2-3 words have doubled or tripled characters. (That last sentence ended with "...wordd has dooubleed or tripled charaaacters" before I fixed it.)

A related problem is that as I've been trying more & more to make my Apple Pencil actions as light as possible, I seem to err in the opposite direction & they don't register at all. Not always, though: sometimes even if I tap quite briskly multiple times, the action won't register at all.

What I've tried so far:

—unplugging the charging cord: there's no difference between cord plugged in or not plugged in

—restarting my device: doesn't fix the problem

—making sure Pencil is always at least 50% charged: doesn't fix the problem

Using my finger only (for typing) does fix it, so it seems to be a Pencil issue, not a screen issue. Either inside the Pencil itself or in its Bluetooth connection. But I really need the Pencil to be functional for making digital art, my main reason for shelling out the big bucks for these two devices; also I much prefer the precision of the Pencil for doing things like placing my cursor in typing.

Any suggestions? Is it possible it's not in the Pencil at all but instead in flukey Bluetooth in my iPad? I listen to music & videos through Bluetooth headphones for hours every day. I do notice a few micro audio drop outs, but only rarely: at most once a day. But micro audio drop outs would be gaps in the Bluetooth pairing. I don't think my Pencil problem is due to gaps in pairing.

Last but not least, is this sort of problem covered by my Apple Pencil warranty? I didn't buy the extended, but my Apple Pencil Pro is still under the free one-year warranty.