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There is O(n^2) issues due to how we store these directories (#6626), so it's good to keep an eye on them and ensure the numbers stay low. The new per-timeline metric `pageserver_directory_entries_count` isn't perfect, namely we don't calculate it every time we attach the timeline, but only if there is an actual change. Also, it is a collective metric over multiple scalars. Lastly, we only emit the metric if it is above a certain threshold. However, the metric still give a feel for the general size of the timeline. We care less for small values as the metric is mainly there to detect and track tenants with large directory counts. We also expose the directory counts in `TimelineInfo` so that one can get the detailed size distribution directly via the pageserver's API. Related: #6642 , https://github.com/neondatabase/cloud/issues/10273