Loosing SSE session from the browser shouldn't break the agent run

[Spikhalskiy]

Describe the bug
Prerequisites:

Web chat UI started with adk web for a simple agent with only a function tool that hangs for 2 minutes.

Reproduction:

1. Submit a request to wait for 2 minutes and wait for tool to start executing
2. Refresh browser window or terminate /run_sse SSE exchnage opened by the browser in any other way
3. Find the tool call in a scrambled state. The trace will mark the completion at the time of SSE session termination; the tool will never complete, and the agent will never return a response. The session is in a strange state.

Expected behavior:

Browser window refresh shouldn't affect the session in any way.

To Reproduce

Start a long-running tool, then refresh the browser window mid-execution: the execution response will never be processed, and no further processing will happen in this Session until a new message is sent.

Expected behavior
Disconnection of the browser SSE session shouldn't break the running execution of the agent / tools.

Screenshots

Before refresh:

After refresh: