docs: add Dify and update Kimi Code guides

[analogpvt]

This PR adds a step-by-step integration guide for Dify and updates the Kimi Code guide to use the new interactive models.dev setup flow.

Changes:

• Dify: Added the dify.mdx (docs) and dify.md (ui) guides, registered its card in integration-cards.tsx, and added Dify SVG brand icon.
• Kimi Code: Updated kimi-code.mdx (docs) and kimi-code.md (ui) to document the new interactive TUI provider configuration.
• Assets: Added setup screenshots in public folders of both apps/docs and apps/ui packages, using relative paths for local hosting.

[coderabbitai]

Walkthrough

Both Kimi Code integration guide files (apps/docs and apps/ui) are updated to document models.dev registry support, replace the manual config.toml setup flow with an interactive provider manager walkthrough, refresh TOML example model blocks, and update the "Why Use LLM Gateway" section to reference GPT-5.5.

Changes

Kimi Code Guide Documentation Update

Layer / File(s)	Summary
models.dev registry introduction apps/docs/content/guides/kimi-code.mdx, apps/ui/src/content/guides/kimi-code.md	Adds a sentence in both files describing Kimi Code CLI's first-class support for the models.dev registry, enabling dynamic LLM Gateway model discovery, capabilities, and pricing without manual TOML edits.
Interactive setup flow, TOML examples, and Why Use LLM Gateway section apps/docs/content/guides/kimi-code.mdx, apps/ui/src/content/guides/kimi-code.md	Replaces the old manual config.toml walkthrough with step-by-step interactive setup (open provider manager → select LLM Gateway → enter API key → choose model with optional Thinking toggle → start coding). Updates Manual Configuration TOML blocks to use claude-3.7-sonnet and deepseek-r1 with consistent capabilities and display_name fields (removing claude-opus-4-6, deepseek-v4-pro, minimax-m3 examples). Moves and updates the "Why Use LLM Gateway" heading and the 210+ models bullet to reference GPT-5.5.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Possibly related PRs

• theopenco/llmgateway#2594: Directly overlaps — also updates the Kimi Code guide's LLM Gateway config.toml examples with DeepSeek/Minimax/Qwen model variants in the same guide documentation.

Suggested reviewers

• smakosh

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Title check	⚠️ Warning	The PR title mentions updating Kimi Code guides, which aligns with the primary changes (rewriting setup flow and documentation), but it also claims to add Dify, which is not reflected in the provided summary of changes.	Update the title to accurately reflect the actual changes: 'docs: update Kimi Code guide with interactive models.dev setup flow' or remove the Dify reference if it's not included in these changes.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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