Use property-based/`proptest` for backend services with arbitrary inputs

[mercy60]

Internal ID: #94

Imported from ISSUES.md via scripts/import-issues.mjs.

Problem Statement. Service functions accept arbitrary inputs; only hand-picked sample tests exist.

Expected Outcome. Cover parsing/serialization edge cases with property tests.

Acceptance Criteria.

• proptest (or fast-check) wired for at least the analytic computation paths.

Files / modules affected.

• backend/src/analytics/, backend/src/multiplayer-queue/

Dependencies. None.

Difficulty / Effort. Medium / M (≈ 1 day).

Labels. testing

[frankosakwe]

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Hello maintainer i would like to work on this issue

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[praise-idise]

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Please I would love to work on this issue, I am confident of fixing it

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[ademolacomfort]

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[Qoder-Undefined]

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I will love to work on this kindly assign

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