@lauraes In Chrome, click the account/profile icon on the right side of the address bar and create another profile just for work. You can skip creating a separate Google account for it and also tell Chrome to create a desktop shortcut for that profile. Then, you can open both profiles at once. Each one will be in its own window. This will allow you to have separate Outlook logins in use at the same time.
You can do the same in Opera. You just have to create the shortcut for the profile manually.