feat: add ClawRouter as a provider for cost-optimized model routing (#11751)

* feat: add ClawRouter as a provider for cost-optimized model routing

ClawRouter is an open-source LLM router that automatically selects the
cheapest capable model for each request based on prompt complexity,
providing 78-96% cost savings on blended inference costs.

Changes:
- Add ClawRouterApi class extending OpenAI adapter
- Add 'clawrouter' provider to the type system
- Add ClawRouter models (auto, free, eco)
- Add ClawRouter provider config with UI setup
- Add ClawRouter logo
- Add documentation (clawrouter.mdx)

Closes #10843

* docs: enhance ClawRouter documentation

- Add ClawRouter to providers overview
- Expand documentation with:
  - Model capabilities configuration
  - Multiple roles setup
  - Troubleshooting section
  - Cost monitoring
  - Comparison with OpenRouter
  - Complexity dimensions explanation

* feat: add ClawRouter to core/llm/llms

- Add ClawRouter.ts extending OpenAI base class
- Register ClawRouter in llms/index.ts

* feat: add User-Agent headers for ClawRouter integration tracking

- Add 'User-Agent: Continue/IDE' header to identify Continue requests
- Add 'X-Continue-Provider: clawrouter' header for routing analytics
- Enhanced documentation with features list

This helps ClawRouter optimize routing decisions based on integration
source and enables better analytics for the Continue community.

* feat: complete ClawRouter integration with full provider support

- Add clawrouter to PROVIDER_HANDLES_TEMPLATING (autodetect.ts)
- Add clawrouter to PROVIDER_SUPPORTS_IMAGES (autodetect.ts)
- Add clawrouter tool support function (toolSupport.ts)
- Add supportsReasoningField and supportsReasoningDetailsField
- Add promptTemplates with osModelsEditPrompt
- Match OpenRouter implementation patterns

* feat: add ClawRouter to VS Code schema, docs nav, and AI SDK

- Add clawrouter to VS Code config_schema.json provider enum
- Add ClawRouter description in config_schema.json
- Add clawrouter to docs.json navigation (top-level providers)
- Add clawrouter to AI SDK PROVIDER_MAP

* docs: add wallet setup and x402 payment documentation

- Add Wallet & Payment Setup section to clawrouter.mdx
- Document payment tiers (free/eco/auto)
- Add wallet funding instructions (Solana/Base USDC)
- Add spend control configuration
- Update VS Code schema description with wallet info
- Update provider longDescription with payment options

* feat: add premium tier and enhanced ClawRouter features

- Add blockrun/premium routing profile (mission-critical tasks)
- Add dual-chain wallet support docs (Base EVM + Solana)
- Add model exclusion documentation
- Update routing profiles table with savings percentages
- Update comparison table with auth/payment differences
- Total 44+ models, 4 routing tiers

* test: add ClawRouter unit tests

- Add ClawRouter.vitest.ts (core/llm/llms)
  - Provider name verification
  - Default options validation
  - Reasoning field support
  - User-Agent header verification
  - Routing profiles acceptance

- Add ClawRouter.test.ts (openai-adapters)
  - Default apiBase
  - Custom apiBase override
  - Continue headers
  - OpenAI standard headers

- Add clawrouter tests to toolSupport.test.ts
  - blockrun/* routing profiles
  - Tool-supporting model patterns

* docs: add routing profile switching and enhanced error handling docs

- Add 'Switching Between Routing Profiles' section with full examples
- Add /model command tip for quick switching
- Add 'Error Handling' section comparing Continue vs ClawRouter
- Document automatic error recovery (429, 402, 500+, timeout)
- Add response header documentation for diagnostics
- Add AI-powered doctor command for troubleshooting

* fix: address PR review feedback - move docs to /more, resize logo, add provider constants, fix docs example

* fix: replace clawrouter logo with higher-res brand kit version (128x128)