fix(web): stop sending prompts into a busy turn on the web UI (#1522)

* fix(web): prevent duplicate first prompts and keep goal drives from looking idle

- Guard startSessionAndSendPrompt with a per-workspace reentry lock so a
  double-click / repeated Enter during draft-session creation cannot fire
  two concurrent first prompts into the same new session.
- Track goal.active in the agent event projector so turn.ended between
  goal-driven continuation turns keeps the session 'running' instead of
  projecting a false 'idle' that drains the local queue into a still-busy
  core (turn.agent_busy).
- Show a 'starting conversation…' loading state on the empty-session
  landing while the first prompt is being created and submitted.
- Persist the resolved model in startSessionAndActivateSkill so the first
  skill turn on a fresh session does not fail with 'Model not set'.

* chore: add changeset for web first-prompt fixes

* fix(web): close remaining first-prompt and goal-settle gaps

- Pass the starting guard through the dock composer: draft-session
  creation selects the new session before submit, which swaps the empty
  composer for the dock; disabling both composers closes the last path
  to a concurrent first POST. Also take the workspace lock in
  startSessionAndActivateSkill / startSessionAndOpenSideChat.
- Emit the owed idle when a goal settles (blocked/paused/completed) in
  the inter-turn gap after a turn.ended was projected as 'running', so
  sending state, in-flight flags and queued prompts flush instead of
  the session staying 'running' forever.

* style(web): fix eqeqeq lint error in first-prompt guard

* fix(web): clear owed idle when a new goal turn starts

The idle debt from a 'running' projection survived turn.started, so an
UpdateGoal('complete'|'blocked') landing mid-turn in the NEXT goal turn
synthesized an early idle. onSessionIdle could then drain queued prompts
into a core that was mid-turn again, re-opening the turn.agent_busy race
for multi-turn goals. Clear the debt on turn.started: from that point the
turn's own turn.ended carries the idle with goalActive already false.

* fix(web): make first-prompt starting state workspace-id-agnostic

isStartingFirstPrompt now reads from the lock set directly (size > 0)
instead of the current activeWorkspaceId. createDraftSession can swap
activeWorkspaceId to a registered id mid-flight; a workspace-keyed read
would then return false while the first prompt is still in the create/
select/submit window, re-enabling the composer and reopening the
duplicate first-submit race.

* revert(web): drop goal-aware idle projection from agentEventProjector

The goalActive / idleOwed shadow state machine grew through multiple
review rounds and still leaves edge cases (snapshot-seeded turns, mid-
turn goal updates). Roll it back to the simple 'turn.ended projects idle'
behavior. Goal-driven sessions can once again race a queued prompt into a
busy core; this is accepted as a known limitation to be resolved properly
in a follow-up that has the core emit an authoritative idle signal.

* chore: align changeset with actual fix scope

* test(web): update profile-patch expectation for model field

.changeset/web-first-prompt-fixes.md

@@ -0,0 +1,5 @@
+---
+"@moonshot-ai/kimi-code": patch
+---
+
+web: Fix an occasional "another turn is active" error when sending the first message of a new conversation, and show a starting state while it is being sent.