A project chat opens only projects your account is on the team of. Anything else comes back as Failed to load project, including a public project you can read perfectly well on its own page.
The test is membership, not authorship. A project you created opens. A project a teammate created and added you to opens, with the same tools on it. Nothing else does.
Why a pasted address fails
The address of a project chat is uni.xyz/unify/project/ followed by the project's identifier, and it looks like something you could hand to anyone. It is not. The chat asks for the project through the same private route the project editor uses, and that route only ever returns projects you are a member of.
So a link to a project you are not on behaves exactly like a link to a project that does not exist. Neither the title nor a single image is revealed, and you cannot tell the two cases apart from the failure. That is deliberate.
What you see when it fails
The chat itself still opens and still works, as a plain chat with no project attached:
- A Failed to load project notice appears.
- The project's name does not appear in the chat.
- The Project Status block at the side is not shown.
- Anything you type is answered as an ordinary conversation.
Reloading will not help. Nothing about the page changes on a second attempt.
Open one from the list instead
The reliable route is the assistant's own project list, which is built from your account rather than from a link. Every project you are a member of appears there, drafts and published work alike, and selecting one opens its chat. Because the list is built the same way the permission check is, anything you can see there will open.
If a project you expect is missing from that list, your account is not on its team. Ask an Admin on the project to add you: see Inviting teammates and collaborating on a project.