Enhance user experience with multiple improvements

- Add username field to right sidebar and mobile modal with 'guest' default
- Implement real-time username sync with URL query string updates
- Add opencompletion.com button and new room creation in left sidebar
- Implement room name slugification (e.g. "a whole new world" → "a-whole-new-world")
- Create shared utils.js for common functions like slugify
- Add single search result auto-redirect functionality
- Remove redundant UI elements ("Create New Room" header, docs link)
- Preserve user settings (username, model, voice) across redirects and room creation

Technical improvements:
- Consolidated duplicate code into shared utility functions
- Enhanced search logic with parameter preservation
- Improved mobile/desktop sync for all input fields
- Better URL handling and query string management

static/js/utils.js

@@ -0,0 +1,12 @@
+/**
+ * Utility functions for the OpenCompletion application
+ */
+
+/**
+ * Convert a string to a URL-friendly slug
+ * @param {string} str - The string to slugify
+ * @returns {string} - The slugified string
+ */
+function slugify(str) {
+    return str.toLowerCase().replace(/\s+/g, '-').replace(/[^\w-]+/g, '');
+}