@Kiogaugio31
Swisscom Webmail (Bluewin) does not have an export function for all mail, only one can be exported in .eml format.
Use a mail program like Thunderbird and save mail locally.
For Windows, there is also a free version of the MailStore Home program, which also allows you to save mail locally on a computer.
MailStore Home - Free Email Archiving & Backup for Home Users