PUB-12 Fix auth startup mirror detection

[rovkinmax]

Task Summary

• Fixes startup behavior after cleared app data so the auth screen starts the OAuth device-code login flow instead of treating the unauthenticated state as KinoPub/API unavailability.
• Adds an explicit authenticated-session check through the auth repository/interactor so AuthVM can separate login-required startup from existing-session API-domain availability checks.
• Preserves API-domain auto-resolution and mirror fallback for existing authenticated sessions and content/API flows.
• Adds AuthVM unit coverage for unauthenticated startup, existing-session fallback, and login-required error handling.

Compliance Review

• Compliance Review passed with no findings.
• Reviewed sources included AGENTS.md, .kent/commands/compliance-review.md, .kent/project-contract.md, PUB-12 body/comment, and the refactor analysis/plan/audit artifacts.
• Reviewed scope was limited to the task-related auth/repository files and the new AuthVM test.

Verification

• git diff --check: passed.
• ./tools/agentw :app:compileDevDebugKotlin :app:testDevDebugUnitTest --tests com.kino.puber.ui.feature.auth.vm.AuthVMTest: passed.

Skipped Checks / Blockers

• No device smoke test was run for this PR.
• No known blockers.