chore(docs): add hasResults to docs_search_v2_search_submitted (#51541)

<!-- claude-slack-attribution -->
_Requested by **Pam Chia** · [Slack
thread](https://supabase.slack.com/archives/C076KTY11DF/p1791767641595649?thread_ts=1791767641.595649&cid=C076KTY11DF)_

## Problem

**Before:** `docs_search_v2_search_submitted` (added in #51146) fires
when a Search V2 query settles on either the `results` or the
`noResults` state, but it only sends `query`. A search that found
nothing looks the same as one that found results, and no other Search V2
event carries the outcome, so the no-results rate for Search V2 can't be
computed.

**After:** the event also sends `hasResults`. It's `true` when the
endpoint returned at least one result and `false` when it returned none,
so zero-result searches can be counted and their queries inspected.

## Solution

- `packages/common/telemetry-constants.ts`:
`DocsSearchV2SearchSubmittedEvent` gains a doc-commented `hasResults:
boolean` property.
- `apps/docs/features/SearchV2/SearchV2Dialog.tsx`: the existing fire
site sends `hasResults: searchState.status === 'results'`. The
`useDocsSearchV2` reducer only sets `results` when the response has at
least one hit, and `noResults` otherwise, so the status is exactly the
outcome.

The change is additive: the event name and `query` are unchanged, and
the `loading`, `error`, and `initial` states still don't fire the event.

Linear:
[GROWTH-1330](https://linear.app/supabase/issue/GROWTH-1330/docs-search-v2-add-hasresults-to-docs-search-v2-search-submitted)

## Review instructions

1. Open the docs preview with the Search V2 flag query:
`?docs-search-v2=search-v2-active`.
2. Open search and type a query that returns results. In the network
tab, the `/platform/telemetry/event` request for
`docs_search_v2_search_submitted` has `custom_properties` `{ "query":
"...", "hasResults": true }`.
3. Type a query that returns nothing (for example random characters).
The event has `"hasResults": false`.

## Checklist

Check all before review:

- [x] I have read
[CONTRIBUTING.md](https://github.com/supabase/supabase/blob/master/CONTRIBUTING.md)
- [ ] If I wrote a new docs topic or edited an existing topic, I used
the `/write-the-docs` or `/edit-the-docs` skill, which applies the docs
[style
guide](https://github.com/supabase/supabase/tree/master/apps/docs/style-guide)
(not applicable: no docs content changed)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

https://claude.ai/code/session_01JaqCdU2sPkBMbaUmUPW75i

---
_Generated by [Claude
Code](https://claude.ai/code/session_01JaqCdU2sPkBMbaUmUPW75i)_

Co-authored-by: Claude <noreply@anthropic.com>

apps/docs/features/SearchV2/SearchV2Dialog.tsx

@@ -82,7 +82,7 @@ function SearchV2Panel({ onResultSelect, onResultOpen }: SearchV2PanelProps) {
     if (searchState.status === 'results' || searchState.status === 'noResults') {
       sendTelemetryEvent({
         action: 'docs_search_v2_search_submitted',
-        properties: { query: searchState.query },
+        properties: { query: searchState.query, hasResults: searchState.status === 'results' },
       })
     }
   }, [searchState, sendTelemetryEvent])

packages/common/telemetry-constants.ts

@@ -1143,6 +1143,10 @@ export interface DocsSearchV2SearchSubmittedEvent {
      * The search term sent to the Search V2 endpoint.
      */
     query: string
+    /**
+     * Whether the Search V2 endpoint returned at least one result for the query.
+     */
+    hasResults: boolean
   }
 }