Fix several problems that led to unexpected results:
* Handle error thrown by box.clt.promote. Not very often but
  it could fail ruining the test. Fixed by retry.
* It's not so obvious but RO server after successful call of
  box.ctl.promote for some time remains RO. On the other hand
  both net.replicaset and the test rely box.info.ro to define
  the leader, for in their view the actual switch to the new
  leader happens some (perhaps different) time after call to
  box.ctl.promote. That asynchrony sometimes led to unexpected
  results. Fixed by waiting of RW status.
* The fix above (wait for RW of the new leader) introduced new
  problem: in case with sequential leader change and broadcast
  of new values, the new leader has good chances (but not 100%)
  to deliver old broadcasted value to the watcher. Fix it by
  splitting the sequence to the leader change with verification
  and broadcast with verification.
* The similar problem happens when a test starts. It may happen
  that all instances are RO, so the initial broadcast on actual
  leader is run with wrong value (that a replica must use).
  Fix it by waiting for a leader to become RW.

Follow-up #9823

NO_DOC=fix flaky test
NO_CHANGELOG=fix flaky test