I'm American, "I'm cleaning my room tonight" as well as "I'm reading a book tonight" are both correct and fine to say. I'm not familiar with the concept of 'arrangement' in this case. You could also say "I'm planning on cleaning my room tonight" this would be an arrangement of sorts?

By adding to a present continuous [ 'I am -ing . .' ] a time in the future [tonight, tomorrow, next Monday, next year, etc.] you make it a statement about the future. Whether it's cleaning your room or reading a book doesn't make a difference. I don’t see the distinction between them that you found on the British Council website.

"Arragement" is defined here as deciding a place and time with somebody else, so basically making a plan with somebody. On the other hand, using "going to" would indicate intention. For that reason you might be more likely to say: "I am going to clean my room tonight." That being said, language is always evolving and I feel like native speakers naturally use these forms interchangeably these days.

It is perfectly natural to say "I'm cleaning my room tonight" so is "I'm reading a book tonight"

The ‘tonight’ makes it an arrangement. Q. What are you doing now? A. I’m cleaning my room. (Now) Q. What are you doing tonight? (In the future) A. I’m cleaning my room. (A plan for the future) I’m cleaning my room tonight. I’m reading ‘War and Peace’ tonight. I’m finishing the book for book club tonight. (All plans for the future)