Add Desearch as an online search and webpage reader provider

[Chkhikvadze]

Describe the feature

Add Desearch as an optional provider for online search and webpage reading, next to the existing providers in src/khoj/processor/tools/online_search.py. Enabled only when DESEARCH_API_KEY is set.

Desearch (https://desearch.ai) is a search API. Verified capabilities used here:

• AI search: one query returns summarized results with source links
• Web search: ranked web results (title, link, snippet)
• X/social search: posts matching a query
• Web crawl: fetch the content of a given URL

Access is either the REST API (https://api.desearch.ai, Authorization: Bearer <DESEARCH_API_KEY>) or the hosted MCP server at https://mcp.desearch.ai/mcp with the same Bearer header. Docs: https://desearch.ai/docs

Use Case

• Users who already have a Desearch key can use it for Khoj online search without another provider account.
• X/social search lets Khoj answer questions about recent public posts, which web results alone often miss.
• Web crawl gives a provider for reading a specific URL.

Proposed Solution

Minimal scope:

• src/khoj/processor/tools/online_search.py: add search_with_desearch(query, location) and read_webpage_with_desearch(web_url, api_key, api_url), following the shape of the existing provider functions; select it when DESEARCH_API_KEY is set.
• documentation/docs/features/online_search.md: one short section with the env var.
• Unit tests with mocked HTTP responses.
  No changes to defaults or other providers.

Additional Information

We (Desearch team) are happy to implement this, add tests and docs, and keep it maintained. We will wait for maintainer feedback before opening a PR.

Link to Discord or Github discussion

(this discussion)