Follow-up to https://github.com/zed-industries/zed/pull/62658

The problematic field is not needed at all in the snapshot, as can be
constructed before starting the scanner — moreover, the field had
accumulated more and more paths between rescans, leaking memory.

Now, we spend more time traversing the entire tree between rescans, but
that happens for rescans only which should be relatively rare?

Release Notes:

- N/A