Update Effect dependencies and examples to 4.0.0-rc.112

[guyowen]

Summary

• coordinate effect, @effect/atom-react, @effect/atom-solid, and @effect/vitest on 4.0.0-rc.112
• update published peer ranges, including the Solid adapter’s solid-js 1.9.14 floor
• migrate all eight examples from Effect v3 and the legacy @effect-atom/* packages to the Effect v4 APIs
• align the examples’ TypeScript and Vite configuration with the updated dependency graph
• document rc.112 installation requirements and add a changeset for all three published packages

Verification

• frozen lockfile installation with lifecycle scripts disabled
• core, React, and Solid typechecks, builds, and 335 tests
• examples TypeScript check and Vite production build
• browser smoke coverage across all eight examples
• packed installation of all three published packages in a strict-peer consumer

[guyowen]

Dependency note: @vitejs/plugin-react moves from v6 to v5 because v6 requires Vite 8, while the examples currently use Vite 6. The v5 line supports Vite 6 and keeps this Effect-focused PR from also becoming a Vite major-version migration. If you would prefer aligning the examples on Vite 8 in this PR, I’m happy to make that change and rerun the full verification.