[Replay] Split up main `index.ts` for better composability

[mydea]

Currently, we have a quite massive index.ts file in replay, which contains a lot of logic.

We should split this up with a few key goals in mind:

1. Separation of concerns - currently, this mixes e.g. the integration itself, the core class for the replay functionality, etc. all together.
2. Functional programming - we try to use a more functional programming style. This does not mean we need to avoid all classes, but a decent amount of stuff can probably be extracted into atomic classes.
3. Avoid very large files - this can make refactorings, understanding etc. harder
4. Declare what is public & private - currently, everything is kind of public, we want to change this.

Progress

• ref(replay): Split replay integration & container class #6407
• Extract functionality from replay container class into atomic functions, where possible
• Ensure everything is correctly declared as public/private

[AbhiPrasad]

Ideally the refactoring should focus on being as bundle size efficient as possible - can we get rid of classes in favor of functions?

[mydea]

Yes, this is def. the goal for the further steps - there is a lot of potential for this here!

[github-actions]

This issue has gone three weeks without activity. In another week, I will close it.

But! If you comment or otherwise update it, I will reset the clock, and if you label it Status: Backlog or Status: In Progress, I will leave it alone ... forever!

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"A weed is but an unloved flower." ― Ella Wheeler Wilcox 🥀

[mydea]

This is mostly done (still room for improvement, but fine for now)