I have exactly the same problem. When clicking the "Start your trial >" button in e-mail, it will not recognise my password which works everywhere else.
I think it assumes I login via a work/school account, which I do not!
Another dead end.
button link is formed like this:
https://emails.azure.microsoft.com/redirect/?destination=https%3A%2F%2Fadmin.microsoft.com%2FAdminPortal%2FHome%3Fref%3Dsubscriptions%2Fwebdirect%2F1f7dba17-edf7-4d35-8d79-46d8....&p=bT01MT....wMDAmdT1hZW8mbD1Ib21l