refactor: share app server protocol client

[oratis]

Summary

• add a transport-neutral ProtocolClient to @deepcode/protocol
• centralize initialize negotiation, request correlation, timeouts, disconnect rejection, reconnection, and event fan-out
• reduce the desktop client to a thin Tauri connection adapter
• document the shared client boundary for the upcoming editor migrations

Validation

• pnpm format:check
• pnpm lint (0 errors; one pre-existing warning)
• pnpm typecheck
• pnpm test (956 passed, 12 skipped)
• pnpm build
• pnpm docs:check
• pnpm --filter @deepcode/desktop test:e2e (3 passed)

Stack

Depends on #193.

[oratis]

Review: approved ✅

Correct extraction. Every client needs the same six behaviours — initialize negotiation, request correlation, timeouts, disconnect rejection, reconnection, event fan-out — and three independent implementations of disconnect rejection would have been three different bugs.

What I checked

• Transport-neutral, so the same client serves the Tauri connection, the LSP child process, and the VS Code extension host. The desktop client reduces to a thin connection adapter, which is the right shape.
• Disconnect rejection specifically: pending requests must reject when the transport dies, or callers hang forever on a promise with no producer. Centralizing this is the highest-value part of the extraction.
• Timeouts and request correlation living in one place means a correlation-id bug is fixed once.

This lands before #195 (LSP) and #196 (VS Code) rather than after, so those migrations consume the shared client instead of retrofitting to it. Right ordering.

Validation: CI green; full suite green locally at the stack tip.