It just works, in my experience, with Narrator on Windows, VoiceOver on macOS and iOS, and TalkBack on Android. The graphical component editor lets you set stuff like labels and tab order and that's usually enough to make things work at least okay with a screen-reader. Getting things to work A+ requires more manual effort, such as implementing AccessibilityHandler for complex components. But the basic JUCE classes are usually much better than what you'd get from any "JavaScript inside WebView" GUI, precisely because you manually coordinate the presentation and the screenreader texts.

I've worked on Surge, which is (to my knowledge) the only fully accessible synthesizer. It uses Juce's a11y abilities to do this work, plus a whole lot of very thoughtful design. We have multiple blind users.