Hello,
Microsoft does not provide an official YouTube desktop app in Microsoft Store for Windows 11. The icon you saw was most likely a website shortcut or a Progressive Web App created through your browser.
To restore it, follow Microsoft supported steps:
If you use Microsoft Edge
• Open Microsoft Edge.
• Go to https://www.youtube.com
• Click the three dots at the top right.
• Select Apps, then Install this site as an app.
• After installation, right click the app in Start.
• Select Pin to taskbar.
If you only want a shortcut
• Open YouTube in Edge.
• Click the three dots.
• Select More tools.
• Choose Pin to taskbar.