"people" is the plural form of "person", i.e. one person, two people, as a group
"people" (pl. "peoples") is a group of people as a unit, e.g. a tribe or an ethnic group or the citizens of a country
"persons" is ALSO the plural of "person" but only used when you talk about individuals rather than a group (e.g. "person of interest" -> "persons of interest", not "people of interest")
Yes this is a bit awkward and yes sometimes what's grammatically possible still sounds awkward even to native speakers (e.g. I'd argue "the polices" is a legitimate term when discussing multiple police organisations of a country as an abstract group but it sounds extremely wrong to most people apparently).
For example, there is a UN Convention on the Rights of Persons with Disabilities. Obviously, native speakers would say "people with disabilities" in almost every situation, but that would be too informal for the title of a treaty.
Likewise, law enforcement use formal speech such as "persons of interest" to bolster their authority, but nobody would ever say "I sat next to two Australian persons on the flight".
Admittedly, it's more likely I'd say "I sat next to two Ozzies on the flight." (No, not Aussies, Ozzies. Like Ozzy Ozbourne. Because that's how it sounds to me when Aussies say 'Aussies.')