[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_config.rs

@@ -1,8 +1,8 @@
 use crate::can_request_original_image_detail;
-use crate::request_user_input_available_modes;
 use codex_features::Feature;
 use codex_features::Features;
 use codex_protocol::config_types::ModeKind;
+use codex_protocol::config_types::TUI_VISIBLE_COLLABORATION_MODES;
 use codex_protocol::config_types::WebSearchConfig;
 use codex_protocol::config_types::WebSearchMode;
 use codex_protocol::config_types::WindowsSandboxLevel;
@@ -33,6 +33,17 @@ pub enum ToolUserShellType {
     Cmd,
 }
 
+pub fn request_user_input_available_modes(features: &Features) -> Vec<ModeKind> {
+    TUI_VISIBLE_COLLABORATION_MODES
+        .into_iter()
+        .filter(|mode| {
+            mode.allows_request_user_input()
+                || (features.enabled(Feature::DefaultModeRequestUserInput)
+                    && *mode == ModeKind::Default)
+        })
+        .collect()
+}
+
 #[derive(Debug, Clone, Eq, PartialEq)]
 pub enum UnifiedExecShellMode {
     Direct,