Refactor managed relay session to idiomatic Effect

[cursor]

What Changed

• Refactored managed relay session token reads to return Option<string> from an Effect-native provider instead of string | null and a local Promise cache.
• Replaced session errors with granular Schema.TaggedErrorClass errors and switched relay timing constants to Duration.
• Updated web/mobile Clerk boundaries to convert their Promise token APIs into Effect/Option at the edge.
• Added TestClock coverage for cached Clerk token expiry and converted touched relay session tests to Effect-native token readers.

Why

This keeps the managed relay session core in Effect end-to-end: cache reuse, concurrent read deduplication, provider refresh, and expiry behavior are now testable with Effect primitives instead of Promise coordination and nullable values.

UI Changes

No UI changes.

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after screenshots for any UI changes
• I included a video for animation/interaction changes

Validation:

• PATH="/home/ubuntu/.nvm/versions/node/v24.17.0/bin:$PATH" pnpm run test -- src/relay/managedRelayState.test.ts from packages/client-runtime
• PATH="/home/ubuntu/.nvm/versions/node/v24.17.0/bin:$PATH" pnpm run test -- src/cloud/managedAuth.test.ts from apps/web
• PATH="/home/ubuntu/.nvm/versions/node/v24.17.0/bin:$PATH" pnpm exec vp check
• PATH="/home/ubuntu/.nvm/versions/node/v24.17.0/bin:$PATH" pnpm exec vp run typecheck
• PATH="/home/ubuntu/.nvm/versions/node/v24.17.0/bin:$PATH" pnpm exec vp run lint:mobile

  

Note

Refactor managed relay session token handling to use Effect and Option types

• Replaces Promise<string|null> with Effect<Option<string>, ManagedRelaySessionError> for readClerkToken across managedRelayState.ts, managedAuth.tsx, and CloudAuthProvider.tsx.
• Introduces ManagedRelaySessionTokenReadError and ManagedRelaySessionTokenUnavailableError as tagged Schema error classes, replacing generic errors for missing session and missing token cases.
• Rewrites token caching in createManagedRelaySession to deduplicate concurrent reads via Deferred, cache tokens until JWT expiry (with a 5s skew), and propagate provider errors through the typed error union.
• Replaces raw millisecond constants with Duration-based constants (DEFAULT_STALE_TIME, DEFAULT_IDLE_TTL, CLERK_TOKEN_EXPIRY_SKEW) in managedRelayState.ts.
• Behavioral Change: callers of setManagedRelaySession must now provide readClerkToken as an Effect returning Option<string> rather than a Promise<string|null>.

^{Macroscope summarized 6ebcdda.}