refactor(tools): update tool exports and main plugin entry

Update tool index exports and main plugin entry point after background-task tool removal.

🤖 GENERATED WITH ASSISTANCE OF [OhMyOpenCode](https://github.com/code-yeongyu/oh-my-opencode)

src/tools/call-omo-agent/tools.ts

@@ -142,7 +142,6 @@ async function executeSync(
         tools: {
           task: false,
           call_omo_agent: false,
-          background_task: false,
         },
         parts: [{ type: "text", text: args.prompt }],
       },

src/tools/index.ts

@@ -1,3 +1,5 @@
+import type { ToolDefinition } from "@opencode-ai/plugin"
+
 import {
   lsp_hover,
   lsp_goto_definition,
@@ -35,28 +37,9 @@ export { createSkillTool } from "./skill"
 export { getTmuxPath } from "./interactive-bash/utils"
 export { createSkillMcpTool } from "./skill-mcp"
 
-import {
-  createBackgroundTask,
-  createBackgroundOutput,
-  createBackgroundCancel,
-} from "./background-task"
-
-import type { PluginInput, ToolDefinition } from "@opencode-ai/plugin"
-import type { BackgroundManager } from "../features/background-agent"
-
-type OpencodeClient = PluginInput["client"]
-
 export { createCallOmoAgent } from "./call-omo-agent"
 export { createLookAt } from "./look-at"
 
-export function createBackgroundTools(manager: BackgroundManager, client: OpencodeClient): Record<string, ToolDefinition> {
-  return {
-    background_task: createBackgroundTask(manager),
-    background_output: createBackgroundOutput(manager, client),
-    background_cancel: createBackgroundCancel(manager, client),
-  }
-}
-
 export const builtinTools: Record<string, ToolDefinition> = {
   lsp_hover,
   lsp_goto_definition,