feat: accept republic built-in tools in core Agent

[frostming]

What & why

bub.core.Agent now accepts republic.tools built-in tools (WebSearch, WebFetch, CodeExecution, ImageGeneration, NativeTool) alongside Tool objects:

agent = Agent(model=model, tools=[my_tool, republic.tools.WebSearch()])

• Function tools stay in agent.tools by name; built-in tools go to the new agent.builtin_tools list.
• Built-in tools are appended to tools on every model call; republic maps them to each API format's native definition (and raises UnsupportedFeatureError for unsupported combinations).
• Providers run them server-side, so they bypass ToolExecutor, BeforeToolCall and prepare_tools. Their calls and results already round-trip through ProviderData on the tape.

Impacted modules

• src/bub/core/agent.py
• tests/test_core_agent.py
• website/src/content/docs/{,zh-cn/}docs/build/sdk.md

Verification

• uv run pytest -q: 616 passed, 20 skipped
• uv run mypy src: clean
• uv run ruff check: clean

🤖 Generated with Claude Code

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Status	Name	Latest Commit	Preview URL	Updated (UTC)
✅ Deployment successful! View logs	bub	6d850dc	Commit Preview URL Branch Preview URL	Oct 14 2026, 02:36 AM