Support reconnects on page refreshes for SSE client connections

[iinozemtsev]

1. reuse reconnection logic between websockets and sse connections
2. persist app instance id on the client side

If we treat reloads as parts of an app lifecycle, it seems natural to preserve an app instance id on full reloads, and looks like a session storage is a good fit.

Fixes #2726.

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[jyameo]

This looks good to me and addresses the breakpoint flakiness. My main concern is ensuring this doesn't regress multi-browser support or standard stability. Please manually verify that page refreshes, hot restarts, and hot reloads all continue to work as expected. In particular, make sure we can open the app in multiple browsers simultaneously and perform hot reloads on all of them without any interference or connection collisions. Since we lack automated tests for the multi-browser scenario, this manual validation is essential.

Thanks @iinozemtsev