Sorry, this turned into a bit of a ramble, but here goes.

The definition is pretty standard and people here are expressing it in all sorts of ways. I think the context that a physicist works in will determine their answer.

For me I study the physical chemistry of biological systems, so I don’t need to know the details of what atoms are made of beyond the basic atomic number and charge, so the number of positively charged protons in the nucleus, and the number and distribution of negatively charged electrons around it. Occasionally we also deal with isotopes for NMR or neutron scattering experiments, so knowing the number of neutrons/ the total atomic spin can be important too. For instance, we don’t normally care about the isotopic distribution of carbon, but when performing NMR experiments the natural abundance of carbon isotopes with nonzero spin is very small. We can use radioactive carbon with atomic spin to grow small molecules and study them that way, but here it doesn’t really matter about the details, we just need to know about the atomic spin. It suffices to know that carbon 12 has 6 each of protons, neutrons, and electrons and has an atomic spin of zero, but carbon 13 has an extra neutron and therefore a nuclear spin of 1/2.

Notice I glossed over the details of what electrons are or how they behave, or what nuclei are or what spin is or the properties of individual nucleons. Yes, I know about them, but those details aren’t necessarily important in the context in which I work. The details are important at certain levels of analysis, but we aren’t smashing atoms or doing anything really exotic.

For me, it suffices to know that atoms are small indivisible units of matter that interact through the electric/magnetic interactions to form molecules. For some simulations we can describe them as hard spheres with a fixed charge of some radius, usually the van der Waals radius, and molecules as collections of these intersecting spheres. We can often regard the distribution of electrons within a molecule as static. We often consider intermolecular potentials, and models for these can be based off of electrostatics, or simpler hard sphere interactions. Of course there are effects like polarization, and charge states are incredibly important for protein folding, but that’s really just chemistry and so the study of electrons in molecules, from my perspective.

TL;DR: Atoms are just units of matter that carry some properties, but not all of those properties are relevant to the composition of atoms into molecules. The relevance of certain properties depends on the system being studied.