Add native Exa web search provider

[kesku]

📝 Description

Adds Exa as a native tools.web / web_search provider. Requests use Exa's POST /search API with type: "auto" and contents.highlights, authenticate via the X-Api-Key header, and support the existing d/w/m/y range filters via startPublishedDate. Includes config, .security.yml key loading, provider selection, UI settings, tests, and documentation.

Enable with tools.web.exa.enabled and an API key, or select explicitly with tools.web.provider = "exa".

🗣️ Type of Change

• 🐞 Bug fix (non-breaking change which fixes an issue)
• ✨ New feature (non-breaking change which adds functionality)
• 📖 Documentation update
• ⚡ Code refactoring (no functional changes, no api changes)

🤖 AI Code Generation

• 🤖 Fully AI-generated (100% AI, 0% Human)
• 🛠️ Mostly AI-generated (AI draft, Human verified/modified)
• 👨‍💻 Mostly Human-written (Human lead, AI assisted or none)

🔗 Related Issue

#2676 (this said the MCP can be used, but now Exa will have native support in PicoClaw!)

📚 Technical Context (Skip for Docs)

• Reference URL: https://docs.exa.ai/reference/search
• Reasoning: Exa is integrated through PicoClaw's existing SearchProvider registry in pkg/tools/integration/web.go, using raw net/http (no new Go module dependency). Keys rotate through the shared APIKeyPool.

🧪 Test Environment

• Hardware: PC
• OS: Linux
• Model/Provider: OpenAI GPT-5.5
• Channels: CLI

📸 Evidence (Optional)

Click to view Logs/Screenshots

Validation performed:

go vet -tags=goolm,stdjson ./pkg/tools/... ./pkg/config/... ./web/backend/...
go test -tags=goolm,stdjson ./pkg/tools/integration/... ./pkg/config/... ./web/backend/... -count=1
golangci-lint run --build-tags=goolm,stdjson ./pkg/tools/... ./pkg/config/... ./web/backend/...
./scripts/lint-docs.sh

Local runtime verification:

Tool call: web_search({"count":3,"query":"site:docs.exa.ai/reference/search Exa Search API documentation"})
Tool execution started ... tool=web_search
Results for: site:docs.exa.ai/reference/search Exa Search API documentation (via Exa)

☑️ Checklist

• My code/docs follow the style of this project.
• I have performed a self-review of my own changes.
• I have updated the documentation accordingly.

[CLAassistant]

All committers have signed the CLA.

[github-actions]

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[kesku]

This PR is still valid!