Polish: extract calculation post-processing from admin panel button

[adrunkhuman]

Problem

CalculateScoresButton.callback in admin_panel/unified_actions.py reaches into private AdminCommands methods across a module boundary: _create_backup() and _post_calculation_to_channel(...). That couples the panel button to AdminCommands internals.

Scope

• Move successful-calculation post-processing behind a public helper/service boundary.
• Let the admin command path and panel button call that public boundary.
• Keep unified_actions.py file structure intact; file size is not the issue.

Acceptance Criteria

• CalculateScoresButton no longer calls private AdminCommands methods.
• Backup and league-channel posting behavior is unchanged.
• Existing cooldown and panel refresh behavior is unchanged.
• Relevant tests pass.