Animated Banner borked in experimental mode

### Describe the bug

The Copilot CLI animated banner used to display inline in the console, and it looked slick af... but with experimental mode enabled, it's now clears the console, and displays near the bottom. It feels very broken like this.

### Normal mode, shows the animated banner inline -- very slick:

### Experimental mode, shows the animated banner at the bottom -- losing all inline context from the console -- no matter what -- it feels pretty borked:

### Affected version

GitHub Copilot CLI 0.0.419-0.

### Steps to reproduce the behavior

1. Initial conditions:
- Windows Terminal is Installed.
- PowerShell 7.x is installed.
- GitHub Copilot CLI is installed.
- In your GitHub Copilot CLI config file: `experimental` is set to `false`.
- In your GitHub Copilot CLI config file: `banner` is set to `always`.
2. Press +**R**
3. Type `pwsh`
4. Press ↵
5. Observe Windows Terminal coming up with PowerShell.
6. Type `copilot.exe`.
7. Press ↵
8. Observe the slick af animation that runs inline, in your shell, preserving the existing terminal text, etc.
9. Type `/Exit`
10. Press ↵
11. Open a new PowerShell 7.x tab in your Terminal.
12. Type `copilot.exe --experimental`.
13. Press ↵
14. Observe the entire console get cleared for no reason, and the banner plays at the bottom of the console, no matter what, looking super jank.

### Expected behavior

The animated Copilot banner should display inline, without clearing the console. 🤘

I feel like it would be okay if the console cleared after the banner animation, (after it goes full screen). But not before. That just looks jank af.

### Additional context

- Bug happens in Windows Terminal, PowerShell 7.x, and copilot experimental mode only.
- ~~In ConHost.exe the screen is always cleared... but the logo appears near the top? Doesn't look awful like that? -- but clearing the screen and hiding it at the very bottom (in Windows Terminal), just looks broken/janky.~~
- Bug also happens in conhost.exe actually (ignore the previous bullet, I accidentally had set `experimental` to `true` in my config for that test; it's the same exact behavior) -- though, again, it doesn't feel as borked in conhost.exe as it does in Windows Terminal.