I've also now tried a potential solution mentioned here
That doesn't seem to have made a difference as well, unfortunately.
Additionally, I've noticed something interesting in the Query Logs for Pi-hole, before there were requests coming from the Docker container running the "ping" to google, apple, and GitHub under localhost (which was expected). Now I no longer see those requests from localhost, starting around the time the power outage took out my network.
Finally, I ran an nslookup within my raspberry pi
nslookup google.com
Server: ::1
Address: ::1#53
Non-authoritative answer:
Name: google.com
Address: 142.250.68.110
Name: google.com
Address: 2607:f8b0:4007:813::200e
And noticed that it's returning an IPv6 address instead of an IPv4 for the DNS server. I think this may be the issue, since Docker doesn't support IPv4. What's confusing me is why this has major impact on the overall performance of the Pihole + Unbound.