Extract Backup Logic into Separate Crate

Description:

The logic for backup should be moved out of `ark-cli` to make it reusable by other applications.

Currently, `ark-cli` implements the backup logic within `ark-cli/src/main.rs` (to be moved to a separate file in #67). Additionally, there is no command to restore backups.

## Proposal:
Create a separate crate to handle the backup and restore logic, including all possible options.

## Benefits:
- **Reusability:** The new crate will be reusable by other crates within the workspace (including `ark-cli`) and by external crates if needed.
- **Maintainability:** The code will be easier to maintain within a dedicated crate rather than being embedded in `ark-cli`.

Start by reading the backup implementation in ark-cli/src/main.rs and the planned extraction context in issue #67. Define the separate crate's backup and restore responsibilities and supported options, then verify that ark-cli and other workspace or external crates can reuse it and that restore is available.

Written by the indexing model from the issue text.