Salesforce Data Export functionality uses the web interface and is not available via API calls, which makes it subject to multi-factor authentication (MFA) settings for standard logins. Data Exports can still be accessed via the SFDC Explorer GUI using OAuth Login as this mechanism supports MFA.
However SFDC Explorer Data Export functionality is not currently compatible with the 'High Assurance' MFA security setting because this causes an additional authentication challenge for each session which requires user intervention. You may wish to create a dedicated user login for Data Exports that does not have this setting enabled. More information: