Can a maintenance workload after a SQL Server reboot cause SQL outage or issue when application load resumes?
If the maintenance tasks were complete, then the resources would be free. If not, then you'll have blocking (unless you have online index rebuilds etc)

My random guess is some client command timeout, which issues an ABORT, which left locks and transactions. Your node failover is the same as closing all connections. The timeout could have been caused by cold cache, no cached query plans etc

Saying that, I have seen brain dead polling process overload a database by opening and closing connection 1000s of times per second. And similar. Or one client needs rebooted , normally indicated by ASYNC_NETWORK_IO waits.

Can you reproduce it though? Which will be tricky on a live system

See SQL Server Transaction Timeout for more (both answers)