build(test-potel-trace-propagation): Migrate backend from pip to uv

Replace backend/requirements.txt with backend/pyproject.toml and update
backend/run.sh to use uv for dependency management and script execution.

Refs PY-2486
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: ericapisani

test-potel-trace-propagation/backend/pyproject.toml

@@ -0,0 +1,17 @@
+[project]
+name = "test-potel-trace-propagation-backend"
+version = "0"
+requires-python = ">=3.12"
+
+dependencies = [
+    "blinker>=1.9.0",
+    "flask>=3.1.0",
+    "gunicorn>=23.0.0",
+    "ipdb>=0.13.13",
+    "markupsafe>=3.0.2",
+    "requests>=2.32.3",
+    "sentry-sdk[flask,opentelemetry-experimental]",
+]
+
+[tool.uv.sources]
+sentry-sdk = { path = "../../../sentry-python", editable = true }

test-potel-trace-propagation/backend/requirements.txt

@@ -1,18 +1,8 @@
 #!/usr/bin/env bash
+set -euo pipefail
 
-# exit on first error
-set -xe
+if ! command -v uv &> /dev/null; then
+    curl -LsSf https://astral.sh/uv/install.sh | sh
+fi
 
-# create and activate virtual environment
-python -m venv .venv
-source .venv/bin/activate
-
-# Install (or update) requirements
-python -m pip install -r requirements.txt
-
-
-# Run Flask application on localhost:5000
-flask --app main run
-
-# Run Flask application with multithreading (port 8000)
-# gunicorn main:app -w 1 --threads 12
+uv run flask --app main run