Add diagnostic instrumentation

Currently we have no diagnostic instrumentation. Performance measures would be useful, especially:

- the rate of lease acquisition
- hold time for leases
- wait time for acquiring leases

We should also look at whether we need to add any error reporting diagnostics, or whether what we get automatically from how use of Azure Storage interacts with Application Insights is sufficient.

No files or tests are identified. Start by tracing the lease lifecycle and reviewing how Azure Storage interacts with Application Insights; define how to measure lease acquisition rate, hold time, and wait time, then decide whether additional error reporting is needed. Done means the diagnostic scope and implementation points are agreed and covered by tests or verification.

Written by the indexing model from the issue text.