fix: ai sidebar closing (#45932)

## TL:DR 

fixes ai assistant panel closing after running queries in logs and
analytics

## b4: 
(thanks to OP)
<img width="2102" height="854" alt="Image"
src="https://github.com/user-attachments/assets/6a1416d8-67bf-4166-999a-d8743746efda"
/>

## after:


https://github.com/user-attachments/assets/bec3366b-b4d6-41c8-a287-f8c37a818f71



## ref: 
- closes https://github.com/supabase/supabase/issues/45930

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **Bug Fixes**
* Improved synchronization between the Logs Explorer editor and the
URL/search state: running a query now updates the shared search state
(and recent snippets) rather than performing a full route push, and the
editor now prioritizes the URL/state value when present to prevent
mismatches during navigation or query execution.

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apps/studio/pages/project/[ref]/logs/explorer/index.tsx

@@ -72,7 +72,7 @@ export const LogsExplorerPage: NextPageWithLayout = () => {
 
   const editorRef = useRef<editor.IStandaloneCodeEditor>()
   const [editorId] = useState<string>(uuidv4())
-  const { timestampStart, timestampEnd, setTimeRange } = useLogsUrlState()
+  const { search, setSearch, timestampStart, timestampEnd, setTimeRange } = useLogsUrlState()
   const defaultHelper = useMemo(() => getDefaultHelper(EXPLORER_DATEPICKER_HELPERS), [])
   const initialDatePickerValue = useMemo<DatePickerValue>(() => {
     if (timestampStart && timestampEnd) {
@@ -217,15 +217,7 @@ export const LogsExplorerPage: NextPageWithLayout = () => {
     } else {
       setTimeRange('', '')
     }
-    const queryParams: Record<string, string | string[] | undefined> = { ...router.query, q: query }
-    if (datePickerValue.isHelper) {
-      delete queryParams.its
-      delete queryParams.ite
-    }
-    router.push({
-      pathname: router.pathname,
-      query: queryParams,
-    })
+    setSearch(query)
     addRecentLogSqlSnippet({ sql: query })
   }
 
@@ -326,10 +318,13 @@ export const LogsExplorerPage: NextPageWithLayout = () => {
   }
 
   useEffect(() => {
-    if (q) {
+    if (search) {
+      setEditorValue(search)
+    } else if (q) {
       setEditorValue(q)
+      setSearch(q)
     }
-  }, [q])
+  }, [q, search, setSearch])
 
   useEffect(() => {
     // prevents overwriting when the user selects a helper.