Source

File: wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php

public function create_item_permissions_check( $request ) {
		if ( ! empty( $request['id'] ) ) {
			return new WP_Error(
				'rest_post_exists',
				__( 'Cannot create existing post.' ),
				array( 'status' => 400 )
			);
		}

		$post_type = get_post_type_object( $this->post_type );

		if ( ! empty( $request['author'] ) && get_current_user_id() !== $request['author'] && ! current_user_can( $post_type->cap->edit_others_posts ) ) {
			return new WP_Error(
				'rest_cannot_edit_others',
				__( 'Sorry, you are not allowed to create posts as this user.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		if ( ! empty( $request['sticky'] ) && ! current_user_can( $post_type->cap->edit_others_posts ) && ! current_user_can( $post_type->cap->publish_posts ) ) {
			return new WP_Error(
				'rest_cannot_assign_sticky',
				__( 'Sorry, you are not allowed to make posts sticky.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		if ( ! current_user_can( $post_type->cap->create_posts ) ) {
			return new WP_Error(
				'rest_cannot_create',
				__( 'Sorry, you are not allowed to create posts as this user.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		if ( ! $this->check_assign_terms_permission( $request ) ) {
			return new WP_Error(
				'rest_cannot_assign_term',
				__( 'Sorry, you are not allowed to assign the provided terms.' ),
				array( 'status' => rest_authorization_required_code() )
			);
		}

		return true;
	}