Does a coordinate clause include a coordinator (/coordinating conjunction)?

Does a coordinate clause include a coordinator (/coordinating conjunction)?

For example:

"It was apple-blossom time, and the days were getting warmer."

Is "and the days were getting warmer" a coordinate clause?
Or is it "the days were getting warmer" (without "and") that is a coordinate clause?
Which does the coordinator "and" belong in?

https://www.thoughtco.com/coordinate-clause-grammar-1689804

In English grammar, a coordinate clause is a clause (i.e., a word group containing a subject and predicate) that is introduced by one of the coordinating conjunctions–most commonly and or but.

Practical English Usage

co-ordinate clause one of two or more main or subordinate clauses of equal ‘value’ that are connected. Examples: Shall I come to your place or would you like to come to mine?; It’s cooler today and there’s a bit o f a wind; she said that it was late and that she was tired. See also main clause, subordinate clause.