[canary] 🚀 Use dataclasses for 3way merging (#28160)

This PR introduces several data classes to better compartimentalise the
data being used in this tool. The previous code relied on a very large
method to do all the operations necessary during patch resolution.

The management of the continuation file is also being overhauled to be
its own code, separate from `PatchFailureResolver`, as the continuation
file also stores things like `working_version` which is not necessarily
part of the merge process.

**Version Type**

This type is being introduced to simplify the operations around version
in Brockit. The code is now easier to understand, and the operations are
grouped.

**Infra Mode**
This new execution mode suppresses the status page, and as a
replacement, provides terminal "keep alive" output, to allow the CI to
be kept alive.

Resolves brave/brave-browser#44690
Resolves brave/brave-browser#44727

Author: cdesouza-chromium