[codex] Move tool specs into core handlers (#21416)

## Why

This is the first mechanical slice of moving tool spec ownership toward
the handlers. `codex-tools` should keep shared primitives and conversion
helpers, while builtin tool specs and registration planning live in
`codex-core` with the handlers that own those tools.

Keeping this PR to relocation and import updates isolates the copy/move
review from the later logic change that wires specs through registered
handlers.

## What changed

- Moved builtin tool spec constructors from `codex-rs/tools/src` into
`codex-rs/core/src/tools/handlers/*_spec.rs` or nearby core tool
modules.
- Moved the registry planning code into
`codex-rs/core/src/tools/spec_plan.rs` and its associated types/tests
into core.
- Kept shared primitives in `codex-tools`, including `ToolSpec`,
schema/types, discovery/config primitives, dynamic/MCP conversion
helpers, and code-mode collection helpers.
- Updated handlers that referenced moved argument types or tool-name
constants to use the core spec modules.
- Moved spec tests next to the moved spec modules.

## Verification

- `cargo check -p codex-tools`
- `cargo check -p codex-core`
- `cargo test -p codex-tools`
- `cargo test -p codex-core _spec::tests`
- `cargo test -p codex-core tools::spec_plan::tests`
- `just fix -p codex-tools`
- `just fix -p codex-core`

Note: I also tried the broader `cargo test -p codex-core tools::`; it
reached the moved spec-plan/spec tests successfully, then aborted with a
stack overflow in
`tools::handlers::multi_agents::tests::tool_handlers_cascade_close_and_resume_and_keep_explicitly_closed_subtrees_closed`,
which is outside this spec relocation.

codex-rs/tools/src/tool_spec.rs

@@ -3,18 +3,13 @@ use crate::JsonSchema;
 use crate::LoadableToolSpec;
 use crate::ResponsesApiNamespace;
 use crate::ResponsesApiTool;
-use codex_protocol::config_types::WebSearchConfig;
 use codex_protocol::config_types::WebSearchContextSize;
 use codex_protocol::config_types::WebSearchFilters as ConfigWebSearchFilters;
-use codex_protocol::config_types::WebSearchMode;
 use codex_protocol::config_types::WebSearchUserLocation as ConfigWebSearchUserLocation;
 use codex_protocol::config_types::WebSearchUserLocationType;
-use codex_protocol::openai_models::WebSearchToolType;
 use serde::Serialize;
 use serde_json::Value;
 
-const WEB_SEARCH_TEXT_AND_IMAGE_CONTENT_TYPES: [&str; 2] = ["text", "image"];
-
 /// When serialized as JSON, this produces a valid "Tool" in the OpenAI
 /// Responses API.
 #[derive(Debug, Clone, Serialize, PartialEq)]
@@ -80,54 +75,6 @@ impl From<LoadableToolSpec> for ToolSpec {
     }
 }
 
-pub fn create_local_shell_tool() -> ToolSpec {
-    ToolSpec::LocalShell {}
-}
-
-pub fn create_image_generation_tool(output_format: &str) -> ToolSpec {
-    ToolSpec::ImageGeneration {
-        output_format: output_format.to_string(),
-    }
-}
-
-pub struct WebSearchToolOptions<'a> {
-    pub web_search_mode: Option<WebSearchMode>,
-    pub web_search_config: Option<&'a WebSearchConfig>,
-    pub web_search_tool_type: WebSearchToolType,
-}
-
-pub fn create_web_search_tool(options: WebSearchToolOptions<'_>) -> Option<ToolSpec> {
-    let external_web_access = match options.web_search_mode {
-        Some(WebSearchMode::Cached) => Some(false),
-        Some(WebSearchMode::Live) => Some(true),
-        Some(WebSearchMode::Disabled) | None => None,
-    }?;
-
-    let search_content_types = match options.web_search_tool_type {
-        WebSearchToolType::Text => None,
-        WebSearchToolType::TextAndImage => Some(
-            WEB_SEARCH_TEXT_AND_IMAGE_CONTENT_TYPES
-                .into_iter()
-                .map(str::to_string)
-                .collect(),
-        ),
-    };
-
-    Some(ToolSpec::WebSearch {
-        external_web_access: Some(external_web_access),
-        filters: options
-            .web_search_config
-            .and_then(|config| config.filters.clone().map(Into::into)),
-        user_location: options
-            .web_search_config
-            .and_then(|config| config.user_location.clone().map(Into::into)),
-        search_context_size: options
-            .web_search_config
-            .and_then(|config| config.search_context_size),
-        search_content_types,
-    })
-}
-
 #[derive(Debug, Clone, PartialEq)]
 pub struct ConfiguredToolSpec {
     pub spec: ToolSpec,