I’ve used a UV light pen for water treatment, and typically scoop water
into the bottle. But will the pen kill any parasites, bacteria, and viruses
that are in the droplets around the rim of the bottle, or does it just kill
those in the water being stirred?
Everything inside the bottle dies, but, no, the droplets of water in the threads and on the outside of the bottle are not disinfected by a UV light device.
But the safest bet: scoop water into your water bottle with something other than the bottle you will drink from.