### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

The "Search by Request ID" input on /ui/?page=logs only filters what's already loaded on the current page. The value is never sent to the backend, so you can't find a log if it's on another page or outside the current date range.

**The request_id is not sent to the API** If you open DevTools (F12) and look at the Network tab while searching, the request to /spend/logs/ui has no request_id parameter. The search is done entirely in the browser on the current page only. The bug is in the UI, not the backend.

The endpoint already supports it:

curl '/spend/logs/ui?start_date=2026-06-01+00:00:00&end_date=2026-06-30+23:59:59&request_id=<ID>' \ -H 'Authorization: Bearer sk-...' Returns the correct log.

### Steps to Reproduce

1. Open /ui/?page=logs 2. Go to page 2, copy any row's request_id 3. Go back to page 1 4. Paste it into "Search by Request ID" 5. No results

### Relevant log output

```shell

```

### What part of LiteLLM is this about?

UI Dashboard

### What LiteLLM version are you on ?

v1.84.0

### Twitter / LinkedIn details

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