fix: fix login button logic in usermenu

[ashert-hsueh]

Changes include:

• Show user avatar in usermenu after successful login (same as on main page)
• Adjust dropdown z-index to ensure it appears above main content

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Project	Deployment	Preview	Comments	Updated (UTC)
involutionhell-github-io	Ready	Preview	Comment	Oct 14, 2025 1:57pm
website-preview	Ready	Preview	Comment	Oct 14, 2025 1:57pm

[Mira190]

preview点击主页登录会报错，大佬再看看能优化吗

[longsizhuo]

是因为web-preview用的是另外一个域名，而我们的GitHub注册返回的是我们正式域名，所以我在prod域名下的preview运行看一下

[Copilot]

Pull Request Overview

This PR fixes the login button logic in the user menu by implementing conditional rendering to show either a user avatar menu or sign-in button based on authentication state. The changes also improve the dropdown's visual layering.

• Converted baseOptions() to async function to fetch user session data
• Added conditional rendering to show UserMenu for authenticated users or SignInButton for unauthenticated users
• Improved dropdown z-index to ensure proper layering above main content

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated no comments.

File	Description
lib/layout.shared.tsx	Added session authentication and conditional user menu rendering
auth.ts	Removed empty line for code cleanup
app/docs/layout.tsx	Updated to handle async baseOptions function call
app/components/UserMenu.tsx	Added z-index styling to dropdown for proper layering

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