I am assuming you are using Secure Pages in the original UI to restrict 'view-only' to these datas, otherwise, the PM would have edit access by OOTB.
I am unaware for the NEW UI using Secure Pages approach at this time.
I was going to suggest creating Calculated attributes - for example Concat(name) for a read-only Project Name. Push this to a custom Blueprint which is assigned to the project. But, just tried that now and these attributes aren't currently available to push over to the Blueprint.
But, you may want to review V15.5.1.1 Preview of New Clarity PPM Phoenix UI Theme