## Why
Core and tools need to request MCP elicitation without constructing
app-server wire payloads. The request should remain a neutral protocol
concept until app-server serializes it for a client.
## What changed
- Switched core and tools to
`codex_protocol::approvals::ElicitationRequest`.
- Derived turn and server context inside core instead of carrying
app-server request types through lower layers.
- Kept the app-server payload unchanged through an explicit boundary
conversion.
- Removed the remaining production app-server-protocol dependency from
tools.
## Stack
This is PR 5 of 6, stacked on [PR
#29723](https://github.com/openai/codex/pull/29723). Review only the
delta from `codex/split-connector-metadata-types`. Next: [PR
#29725](https://github.com/openai/codex/pull/29725).
## Validation
- `codex-core` MCP coverage passed: 87 tests.
- Tools elicitation and app-server round-trip coverage passed.
Adam Perry @ OpenAI
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