build(test-fastapi-root-path): Migrate to uv and pyproject.toml

[ericapisani]

Summary

• Replace pip/requirements.txt with uv/pyproject.toml for dependency management
• Update run.sh to use uv run instead of manual venv creation and pip install
• Remove legacy requirements.txt

Refs PY-2451

Test plan

• Verify pyproject.toml includes all dependencies from the original requirements.txt
• Verify run.sh uses uv run
• Verify requirements.txt is removed

🤖 Generated with Claude Code

[linear-code]

PY-2451

[sentry]

Bug: The script installs uv in a subshell, which doesn't update the parent shell's PATH. The subsequent uv command fails with "command not found".
_{Severity: MEDIUM}

Suggested Fix

Source the installer script instead of piping it to a new shell, for example: source <(curl -LsSf https://astral.sh/uv/install.sh). This will run the installer in the current shell process, allowing it to modify the PATH environment variable. Alternatively, explicitly add the installation directory (e.g., $HOME/.cargo/bin) to the PATH after the installation step.

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-fastapi-root-path/run.sh#L5-L9

Potential issue: The `run.sh` script attempts to install `uv` using `curl -LsSf
https://astral.sh/uv/install.sh | sh`. This command runs the installer in a subshell,
which prevents it from modifying the `PATH` environment variable of the main script's
process. Consequently, the next command, `uv run ...`, fails because the shell cannot
find the `uv` executable. Since the script is configured with `set -euo pipefail`, this
"command not found" error will cause the script to terminate, failing the test for any
environment where `uv` is not pre-installed.

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