/remote fixes for chat state, disablement, and session titles (#312428)

* Fix Copilot CLI mission control remote flows

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

* Refine mission control remote events

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

* Use shared integration id for Mission Control

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

* Fix remote Mission Control session sync

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

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Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>