In 23.08.1, when I create foo.json5, there is no syntax highlighting.
Not sure if it’s fixed in the latest version. If not, I suggest to add ;*.json5 to Scripts/JavaScript. I think it’s good enough considering spec[dot]json5[dot]org
As you’ve probably guessed it’s just something that hasn’t been done yet. And after copying some sample code into Kate and selecting both JSON and javascript syntax highlighting my guess is it will need something special,
Javascript copes with the new stuff ok but doesn’t deal with any normal JSON and that is valid JSON5