fix(core): deliver idle synthetic notices without resuming - #45303

Why

Recording a synthetic status notice with resume: false currently leaves it in the inbox until a later agent run. Callers such as background-job recovery need the notice in durable Session history without starting the model or publishing internal Session events themselves.

What Changes

Session.synthetic({ resume: false }) now delivers an eligible idle steer immediately through the existing inbox-delivery event.

Delivery Boundary

The Session API checks the next steered inbox item under the existing per-Session inbox lock and delivers only the requested notice. It does not invoke the runner's batch promotion operation, so it cannot accidentally consume neighboring user prompts. Retries keep the existing stable-ID reconciliation and first-admission behavior.

Scope

This is a standalone prerequisite for simplifying shell notifications in #44844; it does not modify that PR. User-prompt admission and model execution semantics are unchanged. Immediate user-prompt delivery would require separating runner preparation and pending-work accounting, so that broader redesign is intentionally excluded.

Verification

# packages/core
bun run test
bun typecheck

# packages/sdk, using the repository's isolated-home test wrapper
bun run ../core/script/test.ts test/embedded.test.ts --timeout 15000

# repository root
bun run lint:effect-simplifications

• Full Core suite: 2,310 passed, 16 skipped, zero failures.
• Isolated embedded SDK suite: 14 passed.
• Core typechecking and Effect simplification lint passed.
• Pre-push typechecking passed across all 38 workspace packages.
• The ancillary server fetch suite has three pre-existing OAuth callback-port assertion failures (7 passed, 3 failed). All three reproduce unchanged on base 91028a690be4ae763141878b6c3f57b43c585d80 in an isolated detached worktree.