[1962] Unify frontend API root normalization

[Chris0Jeky]

Summary

• extract the terminal-/api normalization shared by version and realtime paths
• preserve the existing versionApi export/test contract while using the shared utility
• keep /health/live and /hubs/boards suffixes at their existing server-root paths

Proof

• red-first api-root suite failed before the utility existed with the expected unresolved import
• API-root, versionApi, and useBoardRealtime suites: 46 passed
• table coverage includes empty/root-relative/absolute/deployment-subpath/trailing-slash/terminal-/api and substring cases
• npm run lint (8 pre-existing warnings, 0 errors)
• npm run typecheck
• npm run build (known ineffective dynamic-import warning only)
• git diff --check

Refs #1962

No issue close or merge requested; this PR is intentionally left open for review.

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