chore: update launchdarkly-server-sdk to 9.16.0

[kinyoklion]

Summary

Update launchdarkly-server-sdk minimum version constraint from >=9.0.0 to >=9.16.0.

No deprecated APIs found in the example code — the app uses the modern Context API and current SDK patterns.

Tested successfully: SDK initializes and evaluates flags as expected.

Link to Devin session: https://app.devin.ai/sessions/e58d80c462594beca14888a34bf57d15
Requested by: @kinyoklion

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Note

Low Risk
Single dependency floor change with no code edits; low risk unless 9.16+ introduces breaking behavior for this app’s usage.

Overview
Dependency bump only: the Poetry constraint for launchdarkly-server-sdk in pyproject.toml changes from >=9.0.0 to >=9.16.0, so installs resolve to SDK 9.16+.

No application source changes in this diff; the PR description notes the sample already uses current patterns (e.g. Context) and was smoke-tested for init and flag evaluation.

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[devin-ai-integration]

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[devin-ai-integration]

Closing — no version bump needed. Poetry resolves launchdarkly-server-sdk = ">=9.0.0" to the latest (9.16.0), so the example already runs against the current SDK. Per maintainer guidance we don't raise a minimum that's already satisfied.