docs: document omit option for basic auth username/password

[devin-ai-integration]

Summary

Documents the omit: true option on username and password fields in basic auth schemes. Setting omit: true removes the field from the generated SDK's public API and uses an empty string when encoding the Authorization header (e.g., omitting password produces base64("username:")). When both fields are omitted, the Authorization header is skipped entirely.

This option is supported across the major SDK generators (Python, TypeScript, Java, Go, C#, Ruby v2, PHP) — see fern-api/fern#14407 for the Python implementation; the same flags are wired through the IR (usernameOmit / passwordOmit) for the other generators.

Changes:

• fern/products/sdks/snippets/basic-auth-params.mdx — added username.omit / password.omit <ParamField> (the canonical auth-schemes reference, rendered on the generators.yml reference page).
• fern/products/api-def/openapi/auth.mdx — one-liner under the Basic accordion to surface the option, with details deferred to the reference page that the section already links to.

Review & Testing Checklist for Human

• Confirm the encoding behavior described matches what each generator actually emits (sourced from the merged Python PR feat(python): support omitting username/password from basic auth when configured in IR fern#14407 and matches the unreleased changelog entries in the other generators' versions.yml).
• Skim the rendered output on both pages (linked below).

Notes

• No SDK changelog entry needed — per the docs repo knowledge, SDK changelog entries are handled separately.
• The OpenAPI parser (convertSecurityScheme.ts, SecuritySchemeConverter.ts) does not currently extract omit from x-fern-basic; OpenAPI users wire this up via auth-schemes in generators.yml. Happy to file a follow-up to extend the parser if you want x-fern-basic.username.omit to work.

Link to Devin session: https://app.devin.ai/sessions/9a4b0d9b8abc45b79f97ee45e7e1f2e7
Requested by: @devalog

[devin-ai-integration]

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[github-actions]

🌿 Preview your docs: https://fern-preview-devin-1778091767-document-basic-auth-omit.docs.buildwithfern.com/learn

Here are the markdown pages you've updated:

• learn/api-definitions/openapi/authentication