Regarding CUI and ITAR... You state "Export-controlled data such as ITAR technical data is one of the categories of CUI".
Need to be careful here. While CUI can include ITAR (ITAR is one of the categories of CUI), ITAR is not a subset of CUI - I can have ITAR information that is not also CUI. Think of a Venn diagram with CUI and ITAR circles - there is an intersection of them, but the ITAR circle is not a subset of the CUI circle.
As an example, I could develop weapon designs on my own (not under government contract) and seek to sell them outside the US. Those designs would be subject to ITAR, but would not be CUI.
CUI is defined in 32 CFR Part 2002 "Controlled Unclassified Information"; see paragraph 2002.4 “Definitions”, sub-paragraph (h). The key phrase is that CUI "is information the Government creates or possesses, or that an entity creates or possesses for or on behalf of the Government". If the Government does not create it or possess it, and it is not created or possessed on behalf of the Government, it is not CUI.