This article says words do have a property called ambiguity.
The Wikipedia article on ambiguity gives this example:
One could say "I bought herbs from the apothecary". This could mean
one actually spoke to the apothecary (pharmacist) or went to the
It also says
The context in which an ambiguous word is used often makes it evident which of > the meanings is intended.
"Pharmacist" or "pharmacy" have obviously more distinct meaning compared to "apothecary." Contexts might alleviate the ambiguity of each word, but it won't change the fact that there's word-level ambiguity. So words should "have" properties like ambiguity.
According to the article, there's a word lexical ambiguity to refer to the word-level ambiguity of meaning in contrast to syntactic ambiguity and semantic ambiguity. And there's a word polysemy to describe a word being lexically ambiguous. There's also a word polyseme to refer to such words.
Identifying which sense of a word is used in a sentence is called word-sense disambiguation (WSD) in computational linguistics. This term is used like "The human brain is quite proficient at word-sense disambiguation. " in the article.