How to disable displaying newsletters with browser

You can set them as private, please see https://www.thenewsletterplugin.com/documentation/newsletters/newsletters-module/:

Newsletters can be set as private. This means that they should be seen just by subscribers who received them. Hence, the link to the online version contains a token to identify the subscriber, who must have the “confirmed” status to see the content (missing, bounced or unsubscribed people can not see the email).

Regards,
Roberto