[16/44] Enable TS strict mode in sdk-experiments

Description

Part of the strict-mode rollout epic #35932. Enable TypeScript strict mode for the sdk-experiments project.

• Dependency layer: 2 · Internal dependents: 0 · Rollout order: 16 / 44

Note: the original acceptance criteria referenced typescript-strict-plugin, npx tsc-strict, and // @ts-strict-ignore. That approach was dropped by the epic — the plugin was never installed. The ACs below reflect the approach in force, documented in core-web/CLAUDE.md → TypeScript Strict Mode.

Acceptance Criteria

• The six strict flags are present in sdk-experiments's own tsconfig.json:
  forceConsistentCasingInFileNames, strict, noImplicitOverride, noPropertyAccessFromIndexSignature, noImplicitReturns, noFallthroughCasesInSwitch.
• tsc -p libs/sdk/experiments/tsconfig.lib.json --noEmit reports 0 errors.
• tsc -p libs/sdk/experiments/tsconfig.spec.json --noEmit reports 0 errors.
• All errors resolved with explicit types — no new any.
• nx run sdk-experiments:lint, :test and :build pass.
• The enforcement status is recorded — i.e. whether any CI gate actually verifies the strictness.

⚠️ :test does not type-check (isolatedModules: true puts ts-jest in transpile-only mode — see #35948). tsc -p is the acceptance test.

Priority

Medium

Additional Context

One project in the bottom-up rollout tracked by epic #35932.

Start with core-web/CLAUDE.md’s TypeScript Strict Mode guidance and the six flags in libs/sdk/experiments/tsconfig.json. Run the two listed tsc --noEmit commands first, then use nx run sdk-experiments:lint, :test, and :build while resolving reported errors with explicit types. Done means all checks pass, no new any is added, and the enforcement status is recorded.