Add a run-server skill for launching + browser-driving the FastAPI app

This sandbox ships with no Python/Node/Docker/browser and no sudo, so
the bulk of this is setup.sh: bootstrap Python via uv, then get
Playwright's Chromium (and tmux, also missing) working by extracting
their .deb dependencies non-root instead of apt-get install. driver.py
is a small Playwright REPL standing in for chromium-cli, which isn't
available here either.

Also carves out .claude/skills/ from the blanket .claude/ gitignore --
skills are shared project tooling, not personal/local state.

.gitignore

@@ -34,4 +34,8 @@ server/docker-compose.yml
 .idea/
 *.swp
 .DS_Store
-.claude/
+.claude/*
+# ...except Claude Code skills (e.g. agent-run instructions for this
+# app) -- those are project tooling worth sharing, not personal/local
+# state like settings.local.json or worktrees/.
+!.claude/skills/