feat(core-agent): extract pure runtime logic from stage-ui into core-agent (#1524)

Depends on #1487 

## Summary

- Introduce `packages/core-agent` — a new pure-runtime package that
extracts zero-Vue/Pinia algorithmic logic from `@proj-airi/stage-ui`,
following a "compatible facade + core sinking" strategy
- Migrate shared chat types, LLM streaming types, chat hook registry,
session message merge logic, context registry algorithm, and LLM service
utilities into `core-agent`
- `stage-ui` files are preserved as re-exports / thin wrappers — all
external imports, store IDs, and public APIs remain unchanged

## Motivation

`stage-ui` currently mixes pure agent runtime logic (algorithms, type
definitions, stateless utilities) with Vue/Pinia state management and
browser-specific adapters. This coupling makes it hard to:
- Test agent logic in isolation
- Reuse agent algorithms outside of Vue contexts (e.g., server-side,
CLI, other frameworks)
- Reason about the boundary between "what the agent does" vs "how the UI
manages state"

---------

Co-authored-by: autofix-ci[bot] <114827586+autofix-ci[bot]@users.noreply.github.com>
Co-authored-by-agent: Unknown <unknown@example.com>

packages/core-agent/package.json

@@ -0,0 +1,46 @@
+{
+  "name": "@proj-airi/core-agent",
+  "type": "module",
+  "version": "0.9.0-alpha.35",
+  "private": true,
+  "description": "Core agent runtime orchestration for AIRI",
+  "author": {
+    "name": "Moeru AI Project AIRI Team",
+    "email": "airi@moeru.ai",
+    "url": "https://github.com/moeru-ai"
+  },
+  "license": "MIT",
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/moeru-ai/airi.git",
+    "directory": "packages/core-agent"
+  },
+  "exports": {
+    ".": {
+      "types": "./dist/index.d.mts",
+      "default": "./dist/index.mjs"
+    }
+  },
+  "main": "./dist/index.mjs",
+  "types": "./dist/index.d.mts",
+  "files": [
+    "README.md",
+    "dist",
+    "package.json"
+  ],
+  "scripts": {
+    "build": "tsdown",
+    "typecheck": "tsc --noEmit"
+  },
+  "dependencies": {
+    "@proj-airi/server-shared": "workspace:^",
+    "@xsai-ext/providers": "catalog:",
+    "@xsai/model": "catalog:",
+    "@xsai/shared-chat": "catalog:",
+    "@xsai/stream-text": "catalog:"
+  },
+  "devDependencies": {
+    "tsdown": "catalog:",
+    "typescript": "^5.9.2"
+  }
+}