I had assumed that it is apps such as Outlook etc., rather than webmail logins, that would continue to be logged in to the account without being
Once you have changed the email password, email apps and clients such as Outlook will continue to have the old password in their settings. That means they will report errors when attempting to send, receive or delete emails for that account so email apps should not be a problem.
However, if the hacker can discover the new password obviously they would be able to update the settings in Outlook.
Looking back at your first post and seeing that you specifically mention the hacker being able to delete eBay emails makes me realise there is something else I should have suggested in my first post.
Hackers often set up filter rules in the hacked account to delete or autoforward specific emails to hide their activities. Once they have done that the rules remain in operation until you delete them.
Check whether they have done that by the signing into your webmail account and following these steps. If there are any rules or an autoforward you do not recognise you can disable them or preferably, delete them completely:
Hope that makes sense.
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