Catalog searches: record what people look for in the store, on /welcome and from a chat

[keysersoft]

None of our three catalog searches kept a trace. The store and /welcome filter in the browser, and find_connectors (shared /mcp, used from Claude) logged neither its query nor its result. So we could not see which apps people come for and do not find.

What changes

• New product events catalog_search and catalog_search_picked, with new metadata keys query, results and missing.
• Chat (ConnectorSetupService.find): the server records every non-empty query with via: 'mcp', the result count and the returned slugs. It also records missing: the query words no connector mentions anywhere. results alone overstates coverage, because "printify shop" returns the shop connectors while Printify itself is missing.
• Store and /welcome (useCatalogSearchReport): only a settled query is sent, after typing pauses for 1.5 s, when a result is opened, or when the page is left. Prefixes are never sent. results counts matches across the whole catalog (the category chip is ignored), and opening a result sends catalog_search_picked.
• A page can only report via: store | welcome; a client-sent via: 'mcp' is dropped.
• sanitizeSearchQuery: whitespace collapsed, at most 100 characters; a query holding an email address or looking like a pasted key is dropped (the event is kept, without the query).

Reading it

select metadata->>'via' via, lower(metadata->>'query') q, count(*), count(distinct organization_id) orgs
from product_events
where event = 'catalog_search' and created_at > now() - interval '30 days'
  and ((metadata->>'results')::int = 0 or metadata ? 'missing')
group by 1, 2 order by 3 desc limit 50;

Verified

• Backend: full jest suite green (6723 pass), 4 new tests in product-event.spec.ts, 1 in connector-setup.service.spec.ts. tsc and eslint clean.
• Frontend: tsc and eslint clean. Not run against a live cloud stack. The hook has the same settle/flush/pick logic as the website one, which was checked in Chrome (one request per settled query, then the pick).

Companion website PR: HelpCode-ai/anythingmcp-website#311.