As a native Japanese speaker, I find this homonyms concern kind of odd. It’s like asking how Japanese people can speak to each other and understand one another given all the homonyms -- the assumption being that speech alone clearly isn’t enough without written materials with kanji to aid their comprehension.
The obvious way people handle it in speech is by picking words that are clearer in context when homonyms might cause confusion. If you consume any Japanese video content on YouTube etc, it’s very common for speakers to say a homonym, instantly notice the ambiguity, and restate it using a clearer word or brief explanation, which they could, at least in theory, do in no- or low-kanji writing too.
同音異義語の区別に不可欠な漢字の廃止は不可能か？(Is abolishing kanji -- which is essential for distinguishing homonyms -- impossible?)