WebSocket vs SSE vs long polling: decision framework for real-time features

we're building out a new notification system and need to decide on the best technology for real-time server-to-client updates. we expect around 100k concurrent users, mostly mobile web, and need to be mindful of corporate proxy compatibility. the options are webhooks, sse, and long polling. sse feels like a good fit for server-to-client only notifications, as it's simpler than websockets and generally plays better with proxies. but websockets offer full duplex if we ever need to expand. long polling is obviously the most compatible but also the least efficient. what's your decision framework for choosing between these, especially considering scale, mobile client constraints, and proxy concerns? are there scenarios where sse really shines over websockets, or vice versa, for purely server-initiated events?