[AI Gateway] Clarify BYOK authorization headers

[Michael-WhiteCapData]

Summary

Clarifies that AI Gateway substitutes a stored provider key only when the provider authorization header is absent. Adds a DeepSeek BYOK request example that omits Authorization and uses cf-aig-authorization for the gateway.

Fixes #33517.

Documentation checklist

• The change adheres to the documentation style guide.
• If a larger change - such as adding a new page- an issue has been opened in relation to any incorrect or out of date information that this PR fixes.

[cloudflare-docs-bot]

@Michael-WhiteCapData This draft pull request has had no activity for 3 days. It will close after 7 days of inactivity. Transition to ready for review if ready. A codeowner can comment /draft-never-stale to keep it open.

[cloudflare-docs-bot]

Review

✅ No issues found in commit b43e6c0.

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[superhighfives]

Thanks for taking the time to contribute this, @Michael-WhiteCapData.

The information looks great, and super useful. I'd love to get this information incorporated into the article, rather than where it's currently sitting at the bottom. Happy to take this over, unless you wanted to take a pass?

[Michael-WhiteCapData]

Thanks! I took a pass and incorporated the header behavior directly into the Update your applications instructions, then removed the separate callout. The DeepSeek BYOK request remains alongside the other provider examples. The documentation checks and full local build pass.