Is your feature request related to a problem? Please describe.
The probe introduced for #33007 in #71806 issues a ProbeRequest only. While
this provides good coverage of the replication layer, it may be missing other
forms of unavailability such as deadlocked evaluation of read-only commands.

Describe the solution you'd like
Enhance the probe. Once the ProbeRequest has cleared, send a range-spanning read (possibly not an actual read, but something that acquires all latches and requires the lease) and clear the probe only if this returns within a timeout with either success or a credible NotLeaseholderError.

Jira issue: CRDB-12218