The simplest and most common oxocarbons are carbon monoxide (CO) and carbon dioxide (CO2). The general consensus is that they are inorganic (see: Is carbon dioxide organic or inorganic?). The other two oxocarbons reasonably stable under standard conditions although rarely encountered are carbon suboxide (C3O2 or O=C=C=C=O) and mellitic anhydride(C12O9), and Wikipedia says they are organic. Question is whether they were always considered organic (at the time of discovery) or were classified as organic at a later point of time. C3O2 was discovered in 1873 by subjecting carbon monoxide to electric current. A chemist named Otto Diels suggested organic names for the compound but didn't state the year of the naming. C12O9 was apparently obtained in 1830 but properly characterized in 1913 by H. Meyer and K. Steiner. Did they then classify the compound as organic?
No classification scheme in general sciences is perfect, there will always be exceptions, borderline cases, and controversial examples. On the other hand, it makes no difference to the molecules whether humans call them inorganic or organic. "A rose by any other name would smell as sweet" The inorganic/organic classification is as bad as chemical/physical classification. For the sake of historical notes, let us consult two leading treatises of early 1900s. One is the English author Mellor. He wrote a multivolume encyclopediac treatise on "Inorganic and Theoretical Chemistry". It is really amazing that one man did this job! He has a full section on carbon and its sub-oxides. This is volume 5.
For contrast, now refer to another leading inorganic chemistry treatise from Germany, Abegg's Handbuch der Anorganischen Chemie it states, (1892), even though the oxides were discovered before 1892.
Kohlenstoff und Sauerstoff: C bildet mit O zwei Verbindungen: CO Kohlenoxyd; CO2 Kohlendioxyd, Kohlensäure, Kohlensäureanhydrid.
This long section starts as carbon and oxygen: C form with O two compounds: carbon oxide CO; CO2 carbon dioxide, carbonic acid, carbonic acid anhydride.
So it is well established that that carbon oxides, were considered part and parcel of inorganic chemistry. You can also check Sidgwick's two volumes Elements & Their Compounds (1940s-1950s?). I remember seeing carbon suboxides. Most likely, they were not well accepted. I mean how should we label graphene oxide. Is it an organic or inorganic compound?
Anonymous Wikipedia authors (and SE authors) should not be deciding elements on whether a compound is organic or inorganic. Wikipedia is a very good starting place but it is not the end. It cannot replace the books and treatises that exist on the subject written by people who dedicated their lives to chemistry.
As to the Wikipedia quote, "Otto Diels later stated that the more organic names dicarbonylmethane and dioxallene were also correct." A reference is needed. Please someone add:
Diels, O. and Blumberg, P. (1908), Über die Konstitution des Kohlensuboxyds. Ber. Dtsch. Chem. Ges., 41: 1233-1236. https://doi.org/10.1002/cber.190804101232