Jetpack connection is broken after importing a site with All-in-one Migration

### Impacted plugin

Jetpack

### Quick summary

Using All-in-one Migration, I exported a site from Studio and imported it to a new WordPress.com site with the Creator plan. A banner is shown:

The docs tell you to click `Jetpack` > `Dashboard` to resolve this issue. In my first test, there was no `Dashboard` menu item. In the second, even when I click `Dashboard`, I am redirected to the frontend home.

### Steps to reproduce

1. Create a new site in WordPress Studio (it is probably an issue with sites created with the Docker env and elswhere - TBC)
2. Add some content, a page or a post
3. Install All-in-one Migration and export your Studio Site
4. Import that backup into a new WordPress.com Creator site

### A clear and concise description of what you expected to happen.

The Jetpack connection should not need to be fixed. Or at least I should be able to resolve the issue as shown in the docs.

### What actually happened

[screen-capture (13).webm](https://github.com/Automattic/jetpack/assets/6851384/683f648f-911f-4c82-8303-a76b4d18eea4)

### Impact

Some (< 50%)

### Available workarounds?

No and the platform is unusable

### Platform (Simple and/or Atomic)

Atomic

### Logs or notes

_No response_