build(test-asyncio-taskgroup): Migrate from pip to uv

[ericapisani]

Summary

• Replace requirements.txt with pyproject.toml for dependency management
• Update run.sh to use uv run instead of manual venv/pip workflow
• Part of PY-2428 migration effort

Test plan

• Run ./run.sh and verify the FastAPI app starts on port 5000

🤖 Generated with Claude Code

[linear-code]

PY-2430

PY-2428

[sentry]

Bug: The run.sh script installs uv but doesn't update the current shell's PATH, causing the subsequent uv run command to fail with 'command not found'.
_{Severity: HIGH}

Suggested Fix

After the uv installation line, add a command to update the PATH for the current session. For example, add export PATH="$HOME/.cargo/bin:$PATH" or source the appropriate shell configuration file.

Prompt for AI Agent

Review the code at the location below. A potential bug has been identified by an AI
agent. Verify if this is a real issue. If it is, propose a fix; if not, explain why it's
not valid.

Location: test-asyncio-taskgroup/run.sh#L4-L7

Potential issue: The `run.sh` script installs `uv` via a curl pipe to `sh`. However, the
installer only modifies shell configuration files (like `.bashrc`) for future sessions
and does not update the `PATH` for the current, non-interactive shell session.
Consequently, the immediately following command, `uv run uvicorn main:app`, will fail
with a 'command not found' error on any system where `uv` is not already installed and
in the `PATH`.

_{Did we get this right? 👍 / 👎 to inform future reviews.}

[sentry]

Bug: The Python version in .python-version (3.11.11) conflicts with the requires-python = ">=3.12" constraint in pyproject.toml, causing uv run to fail.
_{Severity: HIGH}

Suggested Fix

Align the Python versions. Either update the .python-version file to a version that satisfies >=3.12 (e.g., 3.12.0), or adjust the requires-python constraint in pyproject.toml to include 3.11.11.

Prompt for AI Agent

Review the code at the location below. A potential bug has been identified by an AI
agent. Verify if this is a real issue. If it is, propose a fix; if not, explain why it's
not valid.

Location: test-asyncio-taskgroup/pyproject.toml#L4

Potential issue: The project configuration contains a Python version conflict. The
`.python-version` file pins the version to `3.11.11`, while the `pyproject.toml` file
specifies a requirement of `requires-python = ">=3.12"`. When `uv run` is executed, it
will respect the `.python-version` file, attempt to use Python 3.11.11, and then fail
with an incompatibility error because this version does not satisfy the `>=3.12`
constraint defined in `pyproject.toml`.

_{Did we get this right? 👍 / 👎 to inform future reviews.}