At the moment, a JIRA Cloud export is not directly imported in JIRA Cloud.
The following guide explains the process that an administrator has to go through to achieve the migration: How to restore a JIRA Cloud application backup into another JIRA Cloud application

The Migration is mostly used for Changing the Cloud Instance URL Address or Migrating to a New Cloud Instance that also has a feature request for it: CLOUD-7184

The "JIRA Import" page describes:

Prerequisites

1. An export of your existing JIRA instance.
2. Optionally, compressed copies of:
   <JIRA_HOME>/data/attachments directory. The contents should either have the attachments directory as the top level directory, or the project keys within the attachments directory as the top level directories.
   <JIRA_HOME>/data/avatars directory. The contents should have the avatars directory as the top level directory.
   <JIRA_HOME>/logos directory. The contents should have the logos directory as the top level directory.
3. Please note that your JIRA instance will not have any issues attachments, user avatars or project logos if they are not restored along with your exported JIRA data.

It doesn't mention the additional steps to perform the import.

Feature Request:

JIRA Cloud Imports from Cloud exports should work without manual data manipulation.

All the content is on the zip file and it is always in the same format.
This would avoid additional problems with compressing attachments in different types and confusion: JRA-59603