Epic: Centralising Payment Method Integration

[FangedParakeet]

The goal of this epic is to centralise our integration of new payment methods and payment gateways, so that it is simpler to maintain existing payment methods and add new payment methods in the future. This work was begun in #10098, so see paJDYF-guK-p2 for more context on the results.

The roadmap here is to develop and merge a lightweight PoC framework of how these new integrations will function, iteratively improve this implementation as required, integrate existing payment methods into this framework, and finally to document how new payment methods can be added into this new framework.

This epic will track progress towards these stated goals.