feat: add Jackbox API Logger CLI tool

Standalone tool that connects to a Jackbox room by code, captures all
websocket events, and logs summarized output to console + full JSON to
a JSONL file. Consolidates scattered scripts/ws-probe.js,
ws-lifecycle-test.js, and get-jackbox-player-count.js into one
cohesive debugging tool.

Co-authored-by: Cursor <cursoragent@cursor.com>

.gitignore

@@ -21,6 +21,7 @@ frontend/public/manifest.json
 # Logs
 *.log
 npm-debug.log*
+logs/
 
 # OS files
 .DS_Store