Implement a centralized payment method definition system

[brettshumaker]

Description

Implement a centralized payment method definition system to reduce the complexity of adding and maintaining payment methods in WooCommerce Payments. This will consolidate payment method configurations into a single source of truth, making it easier to add new payment methods and maintain existing ones.

Acceptance criteria

• Implement the PaymentMethodDefinitionRegistry as the central system for managing payment method definitions
• Convert all BNPL payment methods to use the new definition system (issues will be created for each remaining payment method)
• Add comprehensive test coverage
• Ensure backwards compatibility is maintained during the transition

Testing instructions

1. Enable each BNPL payment method in WP Admin and verify:
   • Payment method appears correctly
   • Icons display properly
   • Country/currency restrictions work as expected
   • Payment flows complete successfully
2. Change store currency and country to verify payment method availability rules

Dev notes

• All payment method definitions should follow PSR-4 naming conventions
• Icon generation is part of the build process

Additional context

• Original spike issue: Spike: Centralize payment method configuration #10098
• Related to GrabPay implementation research: Spike: Implementing GrabPay as a new payment method #10011
• Architecture discussion: paJDYF-guK-p2