feat: add opt-in Responses API mode

[anvztor]

• Add use_responses flag to opt into Responses API routing (sync + async).
• Convert chat messages to Responses input and parse Responses output for text/tool calls.
• Add tests covering Responses handling.

Closes #15

Signed-off-by: anvztor anvztor@users.noreply.github.com

[anvztor]

Test Results (Proof)

Unit test (focused)

$ uv --directory vendor/republic run pytest -q tests/test_responses_handling.py
...                                                                      [100%]
3 passed in 0.01s

Unit test (full suite)

$ uv --directory vendor/republic run pytest -q
.......................................                                  [100%]
39 passed in 0.04s

E2E (Bub runtime against gateway)

$ PYTHONPATH=/Users/drej/workspace/dottape-internet/vendor/republic/src \
uv --directory vendor/bub run python - <<'PY'
from pathlib import Path
import asyncio
from bub.app import build_runtime

async def main() -> None:
    with build_runtime(Path('/Users/drej/workspace/dottape-internet'), enable_scheduler=False) as runtime:
        result = await runtime.handle_input('retest-502-2', 'hi')
        print('assistant_output:', result.assistant_output)
        print('error:', result.error)

asyncio.run(main())
PY
assistant_output: Hey! What can I help you build or fix today?
error: None

E2E (direct bub chat CLI)

$ PYTHONPATH=/Users/drej/workspace/dottape-internet/vendor/republic/src \
uv --directory vendor/bub run bub run "hi" --workspace /Users/drej/workspace/dottape-internet --session-id e2e-direct-2
2026-02-26 12:31:14.838 | INFO   | bub.cli.app:run:127 | - | run.start workspace=/Users/drej/workspace/dottape-internet model=<default> max_tokens=<default> allowed_tools=<all> allowed_skills=<all>
2026-02-26 12:31:14.884 | INFO   | bub.core.model_runner:run:89 | bub:28f26a959d652297__64846f03 | model.runner.step step=1 model=openai:gpt-5.3-codex
2026-02-26 12:31:18.486 | INFO   | bub.tape.service:fork_tape:70 | - | Merged forked tape 'bub:28f26a959d652297__64846f03' back into 'bub:28f26a959d652297'
Hey! What can I help you with today?