PAT auth fallback to regular PRs no longer works / unclear behavior in private-preview-disabled repos

First of all, thanks for building `gh-stack` — I've been using it heavily and it has been a huge productivity improvement.

My repository is not yet enrolled in the Stacked PRs private preview, so I'm currently on the waitlist. In the meantime, I've been using `gh stack` primarily for its ability to manage and create regular PRs for a stack of branches. This workflow has been working great so far.

After upgrading from v0.0.5 to v0.0.6, that workflow stopped working because my GitHub CLI is authenticated via a Personal Access Token.

## Environment

- gh-stack 0.0.5 → worked
- gh-stack 0.0.6 → fails
- Authentication: GitHub CLI authenticated with a Personal Access Token
- Repository not enrolled in the Stacked PRs private preview

## Behavior in 0.0.5

`gh stack submit --open` successfully created and synchronized regular PRs after confirming:

```text
⚠ Stacked PRs are not enabled for this repository
Would you still like to create regular PRs? Yes
```

Example output:

```text
✓ Created PR #4654
✓ Created PR #4655
✓ Created PR #4656
```

## Behavior in 0.0.6

The command now exits with:

```text
⚠ Personal access tokens are not supported by gh stack during private preview
Run gh auth login to authenticate with OAuth instead.
```

## Question

Is this an intentional behavior change?

The v0.0.6 release notes mention improved PAT error reporting, but from a user perspective the behavior changed from successfully creating regular PRs to failing entirely.

Should PAT-authenticated users still be able to use the regular-PR fallback workflow when a repository is not enrolled in the Stacked PRs preview, or is OAuth now required for all `gh stack` operations?

Reproduce `gh stack submit --open` with a PAT in a repository without the Stacked PRs preview, comparing v0.0.5 and v0.0.6 behavior. Trace the authentication check and regular-PR fallback entry point introduced in v0.0.6. Done means the intended PAT behavior is established and the fallback either works as before or its OAuth requirement is clearly documented and tested.

Written by the indexing model from the issue text.