Is it possible for customers to register, but only gain access to all areas of the shop after activation?

The control can be managed via the ACRIS Private Shopping plugin and the rule-based redirection feature built in the plugin. In the plugin, a rule can be created that is applied to a specific customer group.
Example:

• Rule: Customer group = Standard
• Action: Redirect to a category, for example "Please wait for activation".

This redirect can be configured under Settings → Extensions → Private Shopping. In this way, only activated customer groups receive access to the desired login area.
In this context, the Shopware merchant registration is often used (can be activated under Settings → Customer Groups). Customers register via a special form for merchants. Until activation, they remain in the standard customer group to which the redirect rule is applied. Only after approval do they gain access to the protected area.