Remove remaining custom prompt support (#16115)

## Summary
- remove protocol and core support for discovering and listing custom
prompts
- simplify the TUI slash-command flow and command popup to built-in
commands only
- delete obsolete custom prompt tests, helpers, and docs references
- clean up downstream event handling for the removed protocol events

codex-rs/protocol/src/custom_prompts.rs

@@ -1,20 +0,0 @@
-use schemars::JsonSchema;
-use serde::Deserialize;
-use serde::Serialize;
-use std::path::PathBuf;
-use ts_rs::TS;
-
-/// Base namespace for custom prompt slash commands (without trailing colon).
-/// Example usage forms constructed in code:
-/// - Command token after '/': `"{PROMPTS_CMD_PREFIX}:name"`
-/// - Full slash prefix: `"/{PROMPTS_CMD_PREFIX}:"`
-pub const PROMPTS_CMD_PREFIX: &str = "prompts";
-
-#[derive(Serialize, Deserialize, Debug, Clone, JsonSchema, TS)]
-pub struct CustomPrompt {
-    pub name: String,
-    pub path: PathBuf,
-    pub content: String,
-    pub description: Option<String>,
-    pub argument_hint: Option<String>,
-}

codex-rs/protocol/src/lib.rs

@@ -5,7 +5,6 @@ pub use agent_path::AgentPath;
 pub use thread_id::ThreadId;
 pub mod approvals;
 pub mod config_types;
-pub mod custom_prompts;
 pub mod dynamic_tools;
 pub mod items;
 pub mod mcp;

codex-rs/protocol/src/protocol.rs

@@ -23,7 +23,6 @@ use crate::config_types::Personality;
 use crate::config_types::ReasoningSummary as ReasoningSummaryConfig;
 use crate::config_types::ServiceTier;
 use crate::config_types::WindowsSandboxLevel;
-use crate::custom_prompts::CustomPrompt;
 use crate::dynamic_tools::DynamicToolCallOutputContentItem;
 use crate::dynamic_tools::DynamicToolCallRequest;
 use crate::dynamic_tools::DynamicToolResponse;
@@ -451,9 +450,6 @@ pub enum Op {
     /// enable/disable state) without restarting the thread.
     ReloadUserConfig,
 
-    /// Request the list of available custom prompts.
-    ListCustomPrompts,
-
     /// Request the list of skills for the provided `cwd` values or the session default.
     ListSkills {
         /// Working directories to scope repo skills discovery.
@@ -595,7 +591,6 @@ impl Op {
             Self::ListMcpTools => "list_mcp_tools",
             Self::RefreshMcpServers { .. } => "refresh_mcp_servers",
             Self::ReloadUserConfig => "reload_user_config",
-            Self::ListCustomPrompts => "list_custom_prompts",
             Self::ListSkills { .. } => "list_skills",
             Self::Compact => "compact",
             Self::DropMemories => "drop_memories",
@@ -1370,9 +1365,6 @@ pub enum EventMsg {
     /// List of MCP tools available to the agent.
     McpListToolsResponse(McpListToolsResponseEvent),
 
-    /// List of custom prompts available to the agent.
-    ListCustomPromptsResponse(ListCustomPromptsResponseEvent),
-
     /// List of skills available to the agent.
     ListSkillsResponse(ListSkillsResponseEvent),
 
@@ -3102,12 +3094,6 @@ impl fmt::Display for McpAuthStatus {
     }
 }
 
-/// Response payload for `Op::ListCustomPrompts`.
-#[derive(Debug, Clone, Deserialize, Serialize, JsonSchema, TS)]
-pub struct ListCustomPromptsResponseEvent {
-    pub custom_prompts: Vec<CustomPrompt>,
-}
-
 /// Response payload for `Op::ListSkills`.
 #[derive(Debug, Clone, Deserialize, Serialize, JsonSchema, TS)]
 pub struct ListSkillsResponseEvent {