Enable the RN Strict TypeScript API

[roryabraham]

Problem

RN 0.80 made the Strict TypeScript API opt-in. We are not using it. RN 0.87 enables it by default.

Solution

While we're waiting for Expo SDK 58 to stabilize, let's work on opting-in to the Strict TypeScript API.

[roryabraham]

I'm wondering if maybe we should try to land #99495 first. It's proving to be a bear of a PR

[roryabraham]

Looks like there's a skill specifically for this npx skills add react-native-community/skills --skill migrate-to-strict-api. I'll give it a spin

[roryabraham]

Bailed out. React Native 0.86 opt-in produced 2944 errors across 420 files, so the Strict API is not enabled.
Kept the dual-compatible rewrites (5 deep imports moved to react-native root exports; NodeHandle and HardwareBackPressEvent inlined). Typecheck passes.
Still blocking a later attempt:

• ReactNativeStyleAttributes in src/components/AlwaysPaintedView/index.native.tsx — private, no root export
• Removed types: AlertStatic, CellRendererProps, ViewToken, ViewabilityConfig, ImageResizeMode, TextInputPasteEventData
• Widespread style/*Instance ref mismatches

react-native-safe-area-context is 5.6.2; Strict API needs >= 5.8.1. Feedback thread: react-native-community/discussions-and-proposals#1015