What tools do I need to carry when riding tubeless?
Anchovies and a fork.

I don't mean that as a snack :) They are actually small "rope plugs" made of butyl rubber that can be plugged through the help of a "fork" when the puncture is more nasty and when you see the air is leaking from the tyre. They are called anchovies in the MTB circle, but they can be used on road tubeless tyres as well. You can read up more about that in this review, where they were tested on road Schwalbe One tyres: https://road.cc/content/review/183575-genuine-innovations-tubeless-tire-repair-kit