Thank you for posting the resolution and glad to know the issue was resolved.
Meanwhile 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: I'm Unable to login to AzureVPNClient anymore due to the error that I keep getting consantly that states "MacTunnelExtension wants to use your credential information stored in your keychain" and it asks for my password. Even after I enter my password which I think is the login password for my machine, it still doesn't login.
Solution: I reinstalled the client again from appstore and cleared the cache by clicking configure and clicked clear saved account . After this it started working.
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.