How much confidence do you place in the scientific theory that ordinary matter is made of discrete units, or 'atoms', as opposed to being infinitely divisible?

Atoms are divisble. It possible to believe that matter is made of atoms and matter is infinitely divisible.

A reasonably accurate rewording is: "Do you believe 'H2O' is a meaningful description of water?".

What the heck does meaningful mean? While we are at seeking meaning: "What's the meaning of life?" I don't think that the word makes specific predictions that would allow you to put a confidence rating on the claim being true.

It's very important to mentally distinguish different classes of statements. If you start giving claims that make no predictions confidence levels you mess up your way of thinking precisely about the world.

The map is not the territory. Asking for the confidence in the belief that the map is the territory is wrong on a fundamental level.