(refactor)ui: Refactoring/simplifying TUI state (#8650)

### Description

Previously, we held the state for the TUI in the sub-components of
`app.rs`. In this PR, we're hoisting those state variables up so we can
have better access to that shared state and create more robust UI.

### Testing Instructions

There two behavioral changes in this PR: 

- Reordering of the task list so that running tasks are first in the
list, then planned tasks, then done tasks.
- We are removing the spinner in favor of the "two arrow" indicator.
Users mentioned that the visual noise was more annoying than helpful, so
let's quiet it down.

Beyond that, you should see no behavioral changes.

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Co-authored-by: Chris Olszewski <[email protected]>