Sure these entities existed. But they did not call themselves literally petty kingdoms, their contemporaries did not call them literally "Petty Kingdoms", arguably the word King was not in the language with that spelling at the time. Some scholarly literature calls them petty kings, other use the term King, subregulus, regulus, ri, brenin, etc. It doesn't matter that most of these terms are cognates or synonym for "king" or "petty king" as long as one is selected that does not literally include the modern English language word "king" which has a very specific and significant intentional in game meaning that does not reflect how these "Kings" are actually implemented in the game! Because King is a design keyword it would be a hostile design decision to call these entities "Kingdoms" in CK3 when a) the designers do have multiple defensible choices about nomenclature and b) there is a nomenclature choice available that does not conflict with how they have chosen to model feudal hierarchy.
There is a problem, in that "rex" is the same title that was used in latin for the kings of Wessex and the kings of the whole of England.
It merely shifts the problem to a different language. They would, likely, have all been using variations of cyning in their anglo-saxon titles, whether as "king of Northumbria" or "king of all the English", or "King of all England".
The irish term "Rí" means several things, depending on what qualifications are put to it. It could be a king of a tribe, a king of several tribes, an overking - who confusingly would potentially be subject to a king of overkings, who would then be subject to the Ard Rí ("High King") - who is actually king tier in game terms. Hardly much better, and confusing when you see 4 or 5 levels of title all based off of the same one word, leaving you again reliant on the portrait frame or other indicators to point out their real tier.
"Duke" is entirely inappropriate for an independent ruler in the British Isles.
The Irish would have used Taoiseach or variants on Rí for the entire scale - the Welsh Tywysog (usually translated as "Prince", but really being any ruler) for independent tribes to full kings. The Scots at various stages styled themselves with equivalent titles, with "Kings of the Isles", "Kings of Strathclyde" and so on. "Kings of Mann", independently, and as vassals of England, Scotland and Norway extended into the 16th century.
Largely, if you were independent you called yourself a King if you could even remotely get away with it.