It hadn’t properly registered yet with Arthur that the council wanted to knock it down" - what's the meaning of register with someone here?
There is a definition for this use of 'register' in the Merriam-Webster Learner's dictionary
4 a [no object] : to be recognized or remembered
It took a moment for what she was saying to register. [=it took a moment before I understood what she was saying]
— often used in negative statements The name didn't register with me. [=I didn't recognize the name]