P1 fixes:
- Fix import paths in background/index.ts (./ -> ../lib/)
- Fix Promise-in-string bug in api-client.ts authenticate()
- Add missing background/service_worker key to manifest
- Copy HTML to public/ so Vite places them in dist
P2 fixes:
- Add notifications permission to manifest
- Make showWarningNotification async with proper await
Co-Authored-By: Paperclip <noreply@paperclip.ing>