Are there any languages in which the, largely Indo-European/PIE, and more compartmentalized parts-of-speech system don't work very well? In particular, I am wondering if there are any languages in which the relationship between a verb and noun to other words in a sentence are largely the same? This then, would make the purpose of a verb and noun largely the same, -or at least their distinction more vague-. The reason I ask is because I am curious as to how, if this exists, it may affect communication within sentences and how it changes the way a sentence may need to be formed.
Sonja Lang's Toki Pona has ambiguity so a word can be interpreted as both a noun and a verb. An example from the documentation is "mi moku" that can be translated as "I eat" or "I am food". "Moku" can also be used as an adjective/compound, e.g., "tomo moku" supermarket or restaurant.
Currently, Wikidata lexemes (the part of Wikidata that describes lexemes) has - perhaps controversially - two different lexemes for "moku": https://www.wikidata.org/wiki/Lexeme:L220707 (noun) and https://tools.wmflabs.org/ordia/L220708 (verb).
Yes: Arabic. This was analyzed in considerable detail very early in the Arabic tradition.. Whether some word counts as a verb or a noun is not due to any inherent or essential nature of the word, but to how it is used. And I'm not talking about homonyms etc. but about really the same word. The canonical examples are the so-called "verbal nouns" and "participles". These western terms are miscategorizations. E.g. "Zaydun Daaribu Amrin" v. "Zaydun Daaribun Amran". here the suffixes -u, -un, -in, -an are case endings. The former would normally be translated "Zayd (is the) striker of Amr" (noun); the latter, either that or "Zayd (is, or was, or will be) striking Amr" (verb). But it depends entirely on context; the best translation in either case could be either an English verb or a noun.
Moral of the story: categories like "noun" and "verb" are neither universal nor scientific. They are Western cultural artifacts.