Brock Harris- I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue: Azure Site Recovery Appliance: Failed to get SSL Server cert and fingerprint
Solution: We attempted to deploy a new Appliance, but registration to the same recovery services vault as the replicated servers fails with error: "Registration of 'Proxy Server' with Azure Site Recovery services failed with error 'AADSTS500011'".
Please go through the attached link for better understanding :- https://zcusa.951200.xyz/en-us/azure/site-recovery/deploy-vmware-azure-replication-appliance-modernized
If you have any other questions or are still running into more issues, please let me know. Thank you again for your time and patience throughout this issue.
Please remember to "Accept Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.