Review and clean up public API surface types

## Context

With the addition of `@microsoft/api-extractor` in #6093, we now have visibility into the public API surface. The tool reports 36 `ae-forgotten-export` warnings — types that appear in public function signatures but are not exported from `index.ts`.

None of these types are documented in the Sentry docs, and no users have reported needing them. TypeScript's structural typing means consumers can pass plain object literals without importing the types explicitly.

## What needs reviewing

For each type, decide whether to **export it** (make it part of the public API) or **mark it `@internal`** (explicitly keep it private).

### Options/config types (used as integration/function parameters)
- `ReactNativeTracingOptions`, `ReactNativeTracingState`, `ReactNativeTracingIntegration`
- `ReactNavigationIntegrationOptions`, `ReactNativeNavigationOptions`
- `ReactNativeClientOptions`, `ReactNativeTransportOptions`, `BaseReactNativeOptions`, `ReactNativeWrapperOptions`
- `ReactNativeErrorHandlersOptions`, `LinkedErrorsOptions`, `BreadcrumbsOptions`
- `MobileReplayOptions`, `MobileReplayIntegration`
- `HermesProfilingOptions`
- `GraphQLReactNativeIntegrationOptions`, `SpotlightReactNativeIntegrationOptions`, `SupabaseReactNativeIntegrationOptions`
- `FeedbackFormProps`, `FeedbackButtonProps`, `ScreenshotButtonProps`, `FeedbackFormTheme`
- `TouchEventBoundaryProps`
- `AppStartIntegration`, `defaultIdleOptions`

### Internal/external types (likely should stay unexported)
- `FeedbackFormState`, `FeedbackIntegration`, `GlobalErrorBoundaryState` — internal component state
- `Replay`, `ReplayConfiguration` — `@sentry/browser` internals
- `HostComponent`, `ViewProps` — react-native types
- `ExpoAssetInstance`, `ExpoImageSource`, `ExpoImageLoadOptions`, `ExpoImageRef` — internal Expo types

## Additional items to review
- `logger` from `@sentry/browser` is exported publicly — is this intentional?