For an alerts system. you would tranditionall build a web page which displays alerts/animatiosn/etc
This web page would then be used in the streaming software the streamers uses as a “browser source”
This would include the alerts within the video.
If you instead output via an Extension in any slot thats fine too.
Not any more “lazy” than having it as a browser source.
Generally speaking all alerts are gonna pop at the same time for every user that has the extension loaded. So I wouldn’t worry about sync.
Twitch studio is pretty limited and provides alert stuff itself. Not sure of the current state of third party support for third party alerts within studio.
There is nothing wrong with your approach.
Personally I just wouldn’t do this as an extension