feat: add web search block functionality and integrate with existing plugins

- Introduced a new web search block plugin to handle web search queries and results.
- Updated copilot, doc block, and pro block plugins to include web search context in AI completions.
- Implemented utility functions for parsing and building web search markdown.
- Enhanced API to support web search requests and responses.
- Added configuration for web search URL and timeout settings.
- Updated size limit checks to account for web search content.

reports/searxng/searxng-engine-report-final-20260609-132939.md

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+# SearXNG final engine timing report
+
+- Generated: 2026-06-09T05:29:38.995723+00:00
+- Diagnostic query: `OpenAI`
+- Enabled engines tested: 9
+- request_timeout: 6.0s
+- max_request_timeout: 8.0s
+- tabs: general, news
+
+| Engine | Shortcut | Elapsed ms | Results | Result engines | Unresponsive | Errors |
+|---|---|---:|---:|---|---|---|
+| 360search | 360so | 572.9 | 5 | 360search | [] |  |
+| crowdview | cv | 970.4 | 40 | crowdview | [] |  |
+| yep | yep | 1236.1 | 20 | yep | [] |  |
+| duckduckgo news | ddn | 1251.7 | 30 | duckduckgo news | [] |  |
+| naver news | nvrn | 1781.1 | 10 | naver news | [] |  |
+| searchmysite | sms | 2062.9 | 10 | searchmysite | [] |  |
+| mwmbl | mwm | 2474.9 | 34 | mwmbl | [] |  |
+| reuters | reu | 3044.4 | 20 | reuters | [] |  |
+| startpage | sp | 3639.6 | 10 | startpage | [] |  |
+
+## Default Search Export Summary
+- Query: `OpenAI`
+- Elapsed: 1351.8 ms
+- Results: 118
+- Result engines: 360search, crowdview, mwmbl, searchmysite, startpage, yep
+- Unresponsive: []