Prevent cache timeouts during long tool calls (#316277)

* Initial attempt. Send dummy user requests every 5 mins

* Modified the probe message

* Modified timeouts

* Removed artificial 2 min delay

* Addressing Copilot suggestions

* Made it configurable

* Make probe limit exp based

* Typo in docstring

* Enabled only for execution subagent

* Changed default number of probes to 1

* Fixed formatting in package.json

* Override userInitiatedRequest to false for probe messages

* Added a subtype keep-alive-probe in telemetry

* Updated telemetry to keep subtype unchanged but use a different source

* Address review: scope keep-alive to Anthropic + current round, constant-1 finishedCb

* Simplify keep-alive endpoint resolution: separate lookup, no flag-off reordering

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Co-authored-by: bhavyaus <bhavyau@microsoft.com>