Function showAuthMethodPicker

showAuthMethodPicker(): Promise<AuthMethod>
Shows the authentication method selection dialog.

Presents user with three authentication options (in display order):
- GitHub OAuth.
- Google OAuth.
- Handle/Password credentials.
AuthMethod also includes "linkedin" for backwards compatibility, but the LinkedIn OAuth option is currently disabled in the picker.
Returns Promise<AuthMethod>
Selected authentication method, or undefined if cancelled.
- Defined in src/ui/dialogs/authMethodSelector.ts:42