Refactor snippets view to Vue

Description

Here's the related technical discovery.

UPDATE: The separate issue with the technical discovery has been created. Please keep the discussion on the discovery there instead of the original comment.

Let's refactor the existing snippets functionality to Vue. GraphQL is also a possibility but has not been confirmed yet.

Requirements

This only involves refactoring the snippets show page.

• User snippets (FE entrypoint)
• Project snippets (FE entrypoint)

The Reaction component will be handled in #36769 (closed)

Tasks:

• Introduce a feature flag.
• Refactor behind the feature flag.
• Create issue to remove feature flag.
• Create MR to remove mark old snippets code as deprecated with a link to the feature flag removal issue.

But Why?

Migrating to Vue will make new features much easier to implement and improve the page's long term maintainability.

What about GraphQL?

If it's decided that the BE should adopt GraphQL then we'll increase the weight of this issue to 7.

It is decided, we will go with GraphQL.