[codex] Improve built-in tool schema docs (#24794)

## Summary
- Clarify default, omission, and bounded behavior across built-in tool
schemas, including unified exec, classic shell, Code Mode exec/wait,
multi-agent, agent job, MCP resource, image, goal, plan, tool_search,
and test-sync fields.
- Convert update_plan status to an enum and add short field descriptions
where the schema previously relied on surrounding context.
- Remove the dedicated permission-approval schema test and keep only
updates to existing expected-spec tests.

## Validation
- Ran `just fmt`.
- Ran `git diff --check`.
- Did not run clippy or tests, per request.

Regression has been eval
[here](https://openai.slack.com/archives/C09GDSP1J9X/p1779905065496949)
and we proved there are no regressions

codex-rs/core/tests/suite/search_tool.rs

@@ -163,7 +163,7 @@ async fn search_tool_enabled_by_default_adds_tool_search() -> Result<()> {
                 "type": "object",
                 "properties": {
                     "query": {"type": "string", "description": "Search query for deferred tools."},
-                    "limit": {"type": "number", "description": "Maximum number of tools to return (defaults to 8)."},
+                    "limit": {"type": "number", "description": "Maximum number of tools to return. Defaults to 8."},
                 },
                 "required": ["query"],
                 "additionalProperties": false,

codex-rs/core/tests/suite/spawn_agent_description.rs

@@ -183,7 +183,7 @@ async fn spawn_agent_description_lists_visible_models_and_reasoning_efforts() ->
     );
     assert!(
         description.contains(
-            "Spawned agents inherit your current model by default. Omit `model` to use that preferred default; set `model` only when an explicit override is needed."
+            "Spawned agents inherit your current model by default. If provided, `model` specifies the model to use for the spawned agent."
         ),
         "expected inherited-model guidance in spawn_agent description: {description:?}"
     );