CB Activity and its Notifications API will eventually support browser notifications. Not sure if you can force that using CB Auto Actions since a lot of storage triggers are done during PHP processing with a redirect immediately following and browser notifications are JS driven so they'd never have a chance to function. You'd need a message queue system similar to Joomlas message queue so a notification could be queued up then pushed to browser on next page load.

We don't have any JSON endpoints for that purpose. Our plans are to eventually convert all endpoints to pure JSON standardized schemas. Next frontend would be mostly or entirely driven by VueJS becoming more like a web application. This would allow native applications to hook into the endpoints easily. That's a long way off though. For now if you wanted a JSON endpoint like that you'd have to entirely implement it yourself.

Are we talking months or years ?

Considering it's a complete rewrite of frontend and nearly completely rewrite of all endpoints I can't really give you any kind of estimate like that since it'll be a gradual process. The plan this year is to roll out usage of VueJS and slowly transition from jQuery to vanilla JS and VueJS along with slowly switching some endpoints to JSON.

We'll also be implementing usage of Symfony components, which will save us a significant amount of time. Some of those components will be implemented this year. We're also planning this year to start rewriting more of our legacy APIs (e.g. rewrite Field APIs). In short CB isn't going to vanish anytime soon if anyone has concerns about that. I've probably got 10 years worth of work in my head alone, lol. We'll keep pushing forward.