Meta-issue tracking follow-up tasks to #6361:

• Remove reconnect argument from Nanny #6383
• Restart worker via Nanny on connection failure #6387
• Consider connection-failure worker closures as safe? #6386
• Add validation to BatchedSend and convert to asyncio #6389
• Eliminate partially-removed-worker state on scheduler (comms open, state removed) #6390
  • Basically Worker may message or reconnect to scheduler while worker is closing #6354