Introduce pipeline subscriptions refactor - Code cleanup

What does this MR do and why?

Introduce pipeline subscriptions refactor. Part 5 of the refactor

Goal of this MR

1. Introduce the refactor and remove the flag
2. Update feature spec coverage (to reflect new UI elements)
3. Remove all legacy code

Part one: !139405 (merged)

Part two: !140812 (merged)

Part three: !141157 (merged)

Part four: !141929 (merged)

Part five: You are here... (final MR)

MR acceptance checklist

Please evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Screenshots or screen recordings

How to set up and validate locally

1. Visit Project > Settings > CI/CD > Expand pipeline subscriptions
2. Try adding a new pipeline subscription, deleting subscriptions etc.
3. Ensure code is cleaned up correctly

Related to #434831 (closed)