The scariest ingredient as I see it is AI. Overproduction of elites is always a destabilizing factor, and much of the well educated workforce may now turn out to be overproduction.
Civilizational collapse occurs when society runs afoul of its basic contract and cannot provide its foundational services anymore. That can mean starvation, it also is given e.g. in the situation of elites running low on trust. Leading to social unrest spinning out of control, or former allies refusing to play along with political shenanigans.
In order to evade catastrophic civilizational collapse, you need viable and timely avenues for course-correction or adaptation. Those are presently being blocked by the very elites profiting from the system they bleed dry.
Not as much of a parallel as people tend to think, but the Roman empire fell apart partly because it was based on the theory of constant outward expansion. If your model, say economic, is based on infinite expansion in a finite arena you'll have trouble.
Other Roman influences on the USA include Christianity and to a lesser extent Judaism (since the major US versions come out of post-Roman Judaism.)
Taking a semi-opinionated swag, the core went from Rome to Constantinople, then Venice, then London.
The European Renaissance and the Enlightenment both used Roman and Greek ideas as inspiration. You can see this in early US architecture, and the models for some institutions such as the Senate. Some of this was ironically as a revolt against English institutions (even though England and Wales were successors of a Roman province).
The early USA's language(s) and Judaeo-Christian heritage are partly products of the Roman Empire. (Spanish most definitely is, and French is. English is heavily influenced by French and Latin.)
By this logic, Turkey is a continuation of the Roman Empire too. See: https://en.wikipedia.org/wiki/Ottoman_claim_to_Roman_success...
At what point does something stop being a continuation of something else?