I would like to know what exactly happens when the DHCP server comes
online again. Will the DHCP server know about the DHCP state held by
my client device along with the granted QoS service? Or will the
device have to be authenticated again in order to avail the QoS
All of this very much depends on what happened to the DHCP server, how 'resilient' it is, and how it was recovered back into service.
Most DHCP servers will record state to disk so they can at least attempt to pick up where they left off. Obviously if that isn't possible, if it's lost all its settings and lease info then all bets are off.
In either case, the client doesn't "authenticate". It instead will continue to use the IP address until one of its "renewal times" arrives then it will attempt to contact the DHCP server that issued its current lease, then if it cannot do that it will attempt to get a new IP address by broadcasting a general DHCP request:
A DHCP client automatically attempts to renew its lease as soon as 50
percent of the lease duration has expired. The DHCP client will also
attempt to renew its IP address lease each time that the computer
restarts. To attempt a lease renewal, the DHCP client sends a
DHCPREQUEST packet directly to the DHCP server from which the client
obtained the lease.
If the DHCP server is available, it renews the lease and sends the
client a DHCPACK packet with the new lease duration and any updated
configuration parameters. The client updates its configuration when it
receives the acknowledgment. If the DHCP server is unavailable, the
client continues to use its current configuration parameters.
If the DHCP client fails to renew its lease the first time, then the
DHCP client broadcasts a DHCPDISCOVER packet to update its address
lease when 87.5 percent of the current lease duration expires. At this
stage, the DHCP client accepts a lease that any DHCP server has