fix(web): preserve running state for queued prompts

[seekskyworld]

Problem

Closes the state-regression slice of #363. When a follow-up prompt was accepted during an active turn, the Web UI unconditionally changed the status from running back to preparing.

Value

Long workflow/subagent turns retain an accurate running indicator while queued prompts wait for admission.

Approach

Centralize prompt-accepted state handling and preserve running when already established; only new work enters preparing, and settled prompts return to idle.

Validation

• node --test --experimental-strip-types tests/web/app-render.test.ts
• git diff --check

Impact

• User-visible behavior: queued prompts no longer regress the status label.
• Model-visible context/tools: none.
• Runtime/lifecycle: presentation-only state correction.
• Persisted config/data: none.
• Compatibility/risk: no protocol changes.

[tt-a1i]

切片正确，但会被 #370 盖掉

已经 running 时保持 running、不从 UI 推断完成，这是对的。没有测试。#370 会改同一批行。请并进 #370（或 #384 的 store），不要单独合，否则后合的会把这份修掉。