### What happened?

In the Request Logs UI, the top-level `Search by Request ID` field appears to be a global Request ID lookup, but it only filters the rows already loaded on the current page.

When a known request exists outside the currently loaded page, entering its Request ID shows `No logs found` even though the request can be found by querying the logs endpoint directly with a `request_id` parameter.

### Expected behavior

The top-level `Search by Request ID` field should perform a server-side lookup using the existing logs endpoint, for example:

`/spend/logs/ui?start_date=...&end_date=...&page=1&page_size=50&request_id=<request_id>`

It should also reset pagination to page 1 and display the returned total/page state from the backend.

### Current behavior

The field filters `filteredLogs.data` on the client side, so it only searches the current page of results. This is confusing because:

- a valid Request ID can show `No logs found`; - the pagination summary can still show the unfiltered total; - users may assume the request was not logged by LiteLLM.

### Why this should be supported

The backend already supports `request_id` on `/spend/logs/ui`. The UI also has backend…