build(test-threading-logger): 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 app runs correctly

🤖 Generated with Claude Code

[linear-code]

PY-2480

PY-2428

[sentry]

Bug: The script installs uv but doesn't update the current shell's $PATH. The subsequent call to uv fails because the command cannot be found, causing the script to exit.
_{Severity: MEDIUM}

Suggested Fix

After installing uv, source the relevant shell configuration file (e.g., source ~/.bashrc) or find the uv binary and call it using its absolute path (e.g., ~/.cargo/bin/uv run ...) to ensure it's available in the current script's environment.

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-threading-logger/run.sh#L4-L8

Potential issue: The `run.sh` script attempts to install the `uv` tool if it's not
present. The installer adds the `uv` binary's location to the `$PATH` by modifying shell
configuration files (e.g., `~/.bashrc`). However, these changes are not sourced by the
currently running script. Consequently, when the script immediately calls `uv run python
main.py`, the shell cannot find the `uv` command because its `$PATH` is not updated.
Since the script uses `set -euo pipefail`, this 'command not found' error causes the
script to exit prematurely on its first run on a clean system.

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