If the WEB is a "pull type" where you get information from yourself, you can say that the notification that sends information at the app's discretion is a "push type". It can be said that the timely provision of information through notifications such as the latest news and event notices is a highly convenient function that is consistent with smartphones that are always connected to the Internet. There are even apps/services that do not work without notification, such as SNS.
However, the characteristics of such notifications may work in a bad direction. Since the information is sent suddenly without considering the recipient's situation, it is not uncommon for other people to see a notification that the content is bad. But you can't stop the notifications completely.
In that case, first consider "Do not show notifications on the lock screen." Even if you inadvertently put your smartphone on the screen, there is no risk that someone will see the notification that arrived. The notification will not be completely lost as it is displayed when unlocked/when operating the smartphone.
If you don't want to see notifications on SNS or emails only, you can also select "Do not display private notification contents". When an SNS message arrives, the notification is displayed, but the sender name and contents are hidden, so it is not a problem for someone to see it. You can keep your privacy because the mail (Gmail) is also displayed as "1 new mail".
To make these settings, open the screen in the order of "Settings" → "Apps & notifications" → "Notification settings" and tap "Display notification contents" (Items may differ depending on the version of the device and Android OS) The names may differ). You can control the notification display more easily than by reviewing the settings for each application.