As regards your BTMail accounts it does matter if you are a BT Broadband or a migrated EE Broadband or BT Premium email customer.
If you are a BT Broadband customer you will use your MyBT and your BTID to access your BT account and various things such your bills etc and you manage your BTMail accounts from there. Your email account will show in your MyBT > Your Products > Email Manage as a "Standard" email account.
If you are an EE customer you will use MyEE or what ever EE call it and your EEID to access your EE Broadband account and various things such as your bills and other things include with your broadband account. There is no option to manage an email account from there because EE do not offer an email service.
However if you moved from BT Broadband to EE Broadband and you had BTMail email accounts you were able to retain those as "Standard" email accounts rather than them being downgraded to BTMail Basic account.
As already mentioned you can not use your MyEE and EEID to manage your BTMail accounts. To do that you will need to use your MyBT and BTID which you used prior to moving to EE even although you are now an EE customer.
This is because of the way the migration from BT to EE, which does not have an email service, is managed.
Rather than customers having their email account downgraded to a Basic account or them having to pay for a Premium an email account in order to keep the account the same as the "Standard" accounts, the email accounts which are still BTMail accounts, remained as "Standard" accounts and are managed through a free BT account which to make things easy is just the MyBT account that the migrating customer had. That MyBT account no longer has billing or any of the other BT services accessible from it.
This will should show the BTMail email accounts as "Standard" however there have been instances when the migration did not go as planned and the email accounts were "downgraded" to a BTMail Basic account with its limitations of only being able to be used as webmail.
Because of all of the above that is why you need to say if you are a BT Broadband or EE Broadband customer or a BT Premium email customer so that the correct advice/checks can be made depending on your answer in order to try and help with any problems.