Have you found that there’s peer-review included when it’s university published?

Not comment-OP, but there are different levels:

• "pre-print" means that it hasn't been submitted yet, hasn't been peer-reviewed yet, and hasn't been accepted yet.
• "post-print" means that it's been peer-reviewed, revised, and the content is ready to publish, but it hasn't been formatted to be in the journal.
• "version of record" is the published version. this is called "camera-ready" if it's waiting to be published.

Depending on the contract signed, the academic ~~scammers~~ publishers will usually let the researcher publish the paper on their own web site or university site or repository like arxiv.org. If it's the pre-print, it may be available before publication, but if it's the post-print or version of record, this may be only after a certain period of time has passed.

The articles published to the journal. That's where the peer review happens. The university will then host a copy of the published paper with open access. The university doesn't peer review this, it just provides the hosting. Often the motivation for doing this is compliance with open access. Many areas have well regarded journals that authors want to publish in that are closed, but the research is funded on the condition of open access.

These papers hosted by the university may have different formatting, but will have the same content. They are often harder to find as the references will be to the same paper published in the journal. Some paper search engines will include links to the university's free access page, but you often have to search separately on a general purpose search engine to find that copy.