[07/44] Enable TS strict mode in utils

Description

Part of the strict-mode rollout epic #35932. Enable TypeScript strict mode for the utils project using typescript-strict-plugin.

• Dependency layer: 1 (0 = leaf library, 10 = top-level app)
• Internal dependents: 12 project(s)
• Rollout order: 7 / 44

All internal dependencies of utils should already be in strict mode before starting (they appear earlier in the rollout order).

Acceptance Criteria

• utils's src is added to the typescript-strict-plugin strict paths config.
• All resulting type errors are resolved (no new any; use explicit types).
• // @ts-strict-ignore is used only where unavoidable, each with a follow-up TODO.
• yarn nx run utils:lint passes (and :build / :test where applicable).
• npx tsc-strict passes for utils.
• yarn nx affected -t build does not break dependents.

Priority

Medium

Additional Context

One project in the bottom-up rollout tracked by epic #35932. Depends on the bootstrap task being merged and on lower-layer projects already being strict.

Start with the typescript-strict-plugin strict paths configuration and the utils project's src. Run npx tsc-strict and yarn nx run utils:lint, then check the applicable build and test targets. Done means utils passes strict checking without new any types, unavoidable ignores have follow-up TODOs, and affected dependents still build.