Attempting to access my contacts list on iCloud

You would have to use a PC to do that. iCloud.com is optimized for computer access, since mobile device support is fragmented at best.

If you are syncing Contacts using iCloud, you can access the contacts in the Contacts app.

go to iCloud.com sign in Apple ID and password if you have 2fa fill that in second icon on the top .

only works on a computer.