Add helper for coercing empty string query params to undefined

[Johnpii1]

Summary

Description
Added a reusable helper coerceEmptyStringQueryParamsToUndefined in src/utils/empty-query-param.utils.ts that converts empty-string values to undefined, collapses empty-array results, and recurses into query record objects.
Applied the helper in the shared public query parser by normalizing the input in parsePublicQuery (src/utils/public-query-parse.utils.ts) before Zod validation so all public endpoints receive consistent query shapes.
Added unit tests in src/utils/empty-query-param.utils.test.ts that assert empty search, verified, and cursor params normalize the same as omitted values and that non-empty strings are preserved.

Testing

Testing
Ran the unit test suite for the new tests with pnpm exec jest src/utils/empty-query-param.utils.test.ts --runInBand, which passed.
Ran eslint on the modified files, which reported no errors (pnpm exec eslint src/utils/empty-query-param.utils.ts src/utils/empty-query-param.utils.test.ts src/utils/public-query-parse.utils.ts).
pnpm build was attempted but failed in this environment due to missing/generated Prisma client type exports unrelated to these changes (known workspace type generation issue).

• pnpm lint
• pnpm build
• pnpm exec prisma generate when schema or generated types changed

Checklist

• Linked issue or backlog item
• No secrets or live credentials added
• Docs updated if setup or env changed
• Change is scoped to one problem

close #379

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