Is there a convenient way to see a query count with this tool?

Try either Query -> WP_Query -> look for [post_count]
or Query -> Post Objects -> Number of Posts (at the top)

I meant the number of DB queries itself. Not posts count.

Sorry I misunderstood. Query -> Saved Queries will show a zero-based array so you could scroll to the bottom to get the last index.

On the front page of recent posts on a test site,
Debug This reports 25,
Debug Queries reports 12,
and Query Monitor reports 12.

It seems I need to compare the results to understand the difference.