Update the logic and storage about isFirstTimeUse and defaultProvider

1. Store isDefault provider and the first time use in local ui state
2. Fix the issue that the default provider should not just be null if
we see the passkey intro screen. (The situation for when we first time
see passkey but already set a default provider) And simply the code
structure

Test: deployed locally

Bug: 262215666
Change-Id: I9ab3752c709e528289442f8514e747bb68348a0b