Dear Chance Pagan,
Greetings. Thank you for reaching out to Microsoft Community. We are glad to assist you.
As per your description, l understand you would like to access Cloud Shell via Exchange Admin Center.
As far as l know, to start work with Exchange Online resources in Azure Cloud Shell, we need to establish a connection to Exchange Online in Azure Cloud Shell with the Connect-EXOPSSession cmdlet.
We can start Cloud Shell from the admin center by clicking on Cloud Shell icon on the top right corner.
Once we start Cloud Shell, enter the Connect-EXOPSSession cmdlet which will let us connect to Exchange Online with managed identity for Azure (MSI) using your current login.

For reference: PowerShell Basics: Want to Use Exchange Online in Azure Cloud PowerShell? - Microsoft Community Hub
If above information doesn't meet your needs, it is suggested to contact our online support directly to start a service request online which will save your time and get accurate instructions. Our technical support will help you find a solution.
- Go to the admin center at https://admin.microsoft.com.
- On the bottom right side of the page, select Help & support.
- At the bottom, select Contact Support.
- Enter a description of your issue, confirm your contact number and email address, select your preferred contact method, and then select Contact me. The expected wait time is indicated in the Contact support pane.
Please feel free to let us know if they resolve this issue for you or not. We look forward to hearing from you.
l appreciate for your understanding and cooperation. Stay safe and healthy.
Sincerely,
Tammy | Microsoft Community Moderator.