For everyone reading this here, I'll just post a reply I got via email from support (after a very lengthy back and forth)
We understand that you created a new Azure DevOps organization and attempted to create a public project after mirroring your repository to GitHub. Based on the screenshot you provided, you are seeing only the Private visibility option when creating a project.
Public project creation is no longer available for newly created Azure DevOps organizations.
This is a recent platform change. Newly created Azure DevOps organizations no longer provide the option to create public projects. As a result:
Only the Private visibility option is available.
The link “Try GitHub” redirects you to GitHub.com, as GitHub is now the recommended platform for hosting public open‑source projects
Additionally, only organizations with the Allow public project policy already enabled can create projects or change the visibility of a project to public. The policy is no longer available to organizations that aren't using it already.
For new Azure DevOps organizations, the ability to create public projects has been deprecated and is no longer available, which is why your organization shows only the private option, even after linking to GitHub.
Because public projects can no longer be created in new organizations:
• The open‑source free CI/CD entitlement (free Microsoft‑hosted parallel jobs) cannot be applied.
This seems to be based on this page in the documentation:
Only organizations with the Allow public project policy already enabled can create projects or change the visibility of a project to public. The policy is no longer available to organizations that aren't using it already. Microsoft recommends using GitHub for all your public project needs.However the form for applying for it is still online and mentioned in this page (emphasis mine):
The free grant of parallel jobs for public projects and for certain private projects in new organizations is temporarily disabled. However, you can request this grant by submitting a request. Existing organizations and projects aren't affected. It can take several business days to process your free tier requests. During certain time periods, processing times might be longer.
Notice it mentions 'certain private projects'. I did submit this form, but I haven't received any reply for two weeks. Also the information is completely contradictory, because 'public projects in new organizations' simply cannot be created.
So if you are coming here trying to try the same, I would advise to simply give up, or somehow manage to get a microsoft support agent on the phone. I am about 95% certain that most of the responses I got via the email support and also in this thread are mostly AI generated from these documentation pages, no one seemed to be able to see if my request was received and no one was actually confident whether what I wanted was possible at all.