Kibana version:
master

Steps to reproduce:

1. Open the logs app.
2. Search for gibberish. Logs UI should render an empty list.
3. Start live streaming.
4. Delete the content of the searchbox while live streaming is running.

Expected behavior:
The log stream should reflect the changes in the searchbox and show all log items.

Possible solution:

One possible way to handle this is to disable the search box if live stream is running, in the same way that we lock the date picker, at least until we tackle #59875