Preserve AuthService in the authentication sheet environment

[MatthewCallery]

Fixes #1397.

Presenting AuthPickerView from a UIKit-hosted SwiftUI view on Mac Catalyst can crash because the sheet's descendants cannot find AuthService, even when the picker has .environment(authService). Explicitly pass the existing service into the primary sheet after its account-conflict and MFA modifiers, matching the explicit injection already used for the nested legacy recovery sheet.

Validation in a consuming UIKit/SwiftUI app, using the patched package based on FirebaseUI 16.1.0:

• Six focused hosted tests passed on iPhone 17 Pro Simulator (iOS 26.5).
• The same six tests passed on Mac Catalyst (macOS 26.6.2).
• The presentation regression checks Apple/Google provider labels, dismissal without account preparation, and simulated successful authentication reaching account preparation.
• The unpatched picker reproduced the missing-AuthService crash on Catalyst and passed on iOS.

Built with Xcode 26.6 (17F113). Real provider OAuth and this repository's full test suites were not run. The diff is one line; no dependency versions are changed.

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[gemini-code-assist]

Code Review

This pull request injects the authService into the environment of the AuthPickerView's navigation stack. I have no feedback to provide.

[demolaf]

Looks good.

There's a flaky CI run that's meant to be fixed in this PR #1394, I'll try to get that merged and then this PR can be rebased.