Carolean or Caroline?

So, with the recent passing of Elizabeth II and the her period of regency dubbed the "second Elizabethan age", it isn't too far for some people in politics to proclaim the new era to be called the "Carolean" derived from Carolus the Latin version whence the French Charles stems, though ultimately from a Germanic word for "man", related to English word "churl", but in the sense of peasant or freeman.

The word "karl" has the meaning of "farmhand" in Danish, thus preserving its ancient meaning.

Truss, in a commeration speech in Parliament, said, according to ITV:

All of us in this House will support him as he takes our country forward to a new era of hope and progress. Our new Carolean age.

The crux of this is how the pronunciation of the word has been transcribed, since the Guardian writes the very same regal adjective as Caroline, where both of these are pronounced /ka.ro.li.en/ rhyming the last syllable with the male name Ian.

Is this the correct way of spelling it, though?

The unwavering automaton that powers the closed captions feature on Youtube, gives us:

our new Carolian age

For the pertinent bit, which leans closer towards the actual Latinate form of the possible adjective. Hansard doesn't thus far seem to have said eulogical gathering's transcription available right now.

We needn't wait for that, however, as Wikipedia gives us Caroline as the proper adjective for the period of regency of Charles III's predecessors.

There we go.