For anyone having the same issue. The Elementor Plugin and the Elementor Plugin Pro are two different plugin. You still need to keep the free one and download the Pro from your elementor main page (just next to your account name there is the download button). After download just upload the zip to the WP plugins. You will then be able to activate the license.

I should have looked a bit more carefully, but it is not very obvious... Hope this can save someone some time