feat(sponsors): add Fluxion AI

[KnockOutEZ]

Stacked on #638.

Adds Fluxion AI as a sponsor. Draft until the sponsorship starts; merge after #638.

• Registry entry, logos (light and dark), the README header and sponsors section, SPONSORS.md and the site — each through its own counted /go/fluxion/ hop, so clicks report per placement.
• A labeled sponsored setup example: Fluxion AI as the OpenAI-compatible provider for answer synthesis, in the configuration docs and as examples/llm-synthesis-fluxion, with how to swap in any other provider.

Test plan

• Sponsor link and logo tests, site tests, typecheck, production build
• /go/fluxion/ forwards to the sponsor URL with its own parameters kept and utm_content added
• Run the example against a live Fluxion AI key before merging

If #640 (Helodata) merges first, rebase this onto #638's branch — both add a registry entry, README and SPONSORS.md block, keep both.

[coderabbitai]

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