Found this while testing a bug of AT'ing a site, not related to this.
Nothing, in fact. The plan is there, the site should be made public without entering this flow. If it would, it should go to the Domain step (i saw the skip button there) and then it should recognize that a Business Plan is already in place.
The flow appeared as if the user had a Free Plan on their site.
I tested this as well, one thing I noticed is particular is that, the Keep this plan
string is attached to the free plan CTA irrespective of what plan the site has. In @mlaetitia's test it can seen that the flow shows Keep this plan
on free plan, instead of WordPress.com Business plan.
Likewise on my test, happened on WordPress.com Blogger Plan.
On that note, I am tagging this as a bug and I am attaching a high priority as well - given that this affects everyone now.
Thanks for filing this bug @mlaetitia! You're right that the plans screen should not be shown, if someone already has a plan, but it is intentional to ask people to register a domain when they launch their site if they don't already have one. I created a Trello card for the onboarding team that owns this part of the flow: https://trello.com/c/3dgT6ZyC/639-bug-plans-in-launch-flow-for-paying-customers
Also adding that in my testing, once I selected the Business Plan again, I was stuck at the create site screen on this URL: https://wordpress.com/start/launch-site/launch - there were no console errors either.
Moving out of high priority since Private by Default is turned off for now. We can revisit once that flow is enabled later.
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Thanks for filing this bug @mlaetitia! You're right that the plans screen should not be shown, if someone already has a plan, but it is intentional to ask people to register a domain when they launch their site if they don't already have one. I created a Trello card for the onboarding team that owns this part of the flow: https://trello.com/c/3dgT6ZyC/639-bug-plans-in-launch-flow-for-paying-customers