The Veeam restore process that allows for custom scripting to be run before returning a server to production is Staged Restore. This feature enables administrators to perform necessary operations, like running a script to remove customer photos, during the restore process before the VM is brought back online.References:Veeam Backup & Replication User Guide, Veeam Staged Restore Guide

The feature that is unique to Veeam Agent for Linux and not available in other Veeam Agent configurations is C: Backup from native snapshots. Veeam Agent for Linux includes the ability to leverage native snapshot capabilities of the Linux kernel, such as LVM (Logical Volume Manager) snapshots or Btrfs subvolume snapshots, to create consistent point-in-time copies of data. This capability allows for application-consistent backups even in complex Linux environments, ensuring that data is captured in a consistent state without the need for custom scripting or downtime. Native snapshot support in Veeam Agent for Linux enhances the flexibility and reliability of backups, particularly in environments where Linux-based applications and databases are critical to business operations.

The REST API through Veeam Backup and Replication Server is the available API for automating Veeam Backup and Replication operations. This API enables programmatic control over Veeam Backup & Replication and allows for integration with external systems and custom automation scripts.References:
Veeam Backup & Replication RESTful API Reference, Veeam Automation and Scripting Guide

Explanation
According to the Veeam Agent for Linux User Guide1, Veeam Agent for Linux lets you use the Veeam Recovery Media - a recovery image of the Linux OS that provides an alternative way to boot your computer.
The recovery image is an ISO file that you can burn to a CD/DVD or write to a USB flash drive.