New file watcher implementation removes watchers before consolidated watcher is created

There is a small problem here that by creating a new file watcher after we removed the other ones, the process of consolidation makes a temporary window where we may not get a notification at all.

_Originally posted by @jasonmalinowski in https://github.com/dotnet/roslyn/pull/83101#discussion_r3140999762_

Start by locating the new file watcher implementation and the consolidation path referenced in the issue. Trace the sequence that removes existing watchers and creates the consolidated watcher, then identify or add coverage for the notification gap. Done means consolidation does not leave a window where file changes can go unreported.

Written by the indexing model from the issue text.