fix: keep ACP authentication input runnable during login

[Dante-dan]

Related issue

Closes #505

Problem / pressure

Local ACP authentication starts and their input submissions share the default serial message queue. A login waits for a method selection while that selection waits behind the login, causing the submission timeout reported for Google Antigravity. Authorization-code submissions and cancellation have the same dependency.

Summary

Give each machine/authentication request separate start and follow-up execution lanes. Keep follow-up actions ordered with each other and preserve existing session queue behavior. Add deterministic regressions to the existing message processor suite and document the decision in both languages.

Visual explanation

Before: default lane = start (await input) → submit-input (cannot run)
After:  auth/request/start = start (await input)
        auth/request/input = submit-input / submit-code / cancel

Before / after

Before	After
Login holds the queue needed to submit its selected method or authorization code.	Follow-up requests execute while login is pending.
Cancellation waits behind the login it should cancel.	Cancellation uses the follow-up lane.

Test plan

• Existing message processor suite: 5 passed. The three new submit-input, submit-code, and cancel cases fail against the previous implementation and pass after the change.
• Oxfmt check for both changed TypeScript files and git diff --check passed.
• pnpm check failed during workspace typechecking because package dependencies are absent in this worktree (packages/ignore: missing Node/Vitest types). pnpm format failed because workspace Oxfmt was unavailable; the changed files were formatted and checked with the existing installed formatter. pnpm run docs check reported existing links into uninitialized ACP submodules.

Context handoff

Original user prompt

Show original prompt

请跟进对应的 issue: xxx , 并注意 xxxx 内容

Delegated task scope

The user authorized filling the issue and focus placeholders in the template above. The resulting task scope, filled by the assistant, is: follow #505, fix local authentication input being queued behind the login waiting for it, preserve existing ACP and session ordering behavior, and run the repository checks.

Shared conversation

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