You have to build a proper PWA with a fully formed manifest.json first off. Web Push (i.e: Push Notifications) are fully supported on both iOS and Android. The Only thing that doesn't work is "background" work (but preactically speaking I haven't really needed it).
If you'd like to find out how I build Mobile-first apps with Go, HTML and HTMX hit me up.
Any chance you could write a hello world repo of this stack and post a link here?
Try asking this question to an LLM. (No, seriously.)
Or to a search engine: https://share.google/dTJmGU38xw0kDSJlZ