Task.initでselfを直接参照しても循環参照起こらないことを示すコード

TaskInitViewController.swift

//
//  TaskInitViewController.swift
//  TaskInit
//
//  Created by satoutakeshi on 2022/08/07.
//

import UIKit

class TaskInitViewController: UIViewController {
    var number: Int = 0
    var clouser: () -> () = {}
    var task: Task<Void, Error>?
    override func viewDidLoad() {
        super.viewDidLoad()
        task = Task {
            print(Date().description)
            //try await Task.sleep(nanoseconds: 3 * NSEC_PER_SEC)

            try Task.checkCancellation()

            await Task.sleep(7 * NSEC_PER_SEC)
            //try Task.checkCancellation()

            if Task.isCancelled {
                // 独自のキャンセル処理
                //
                throw CancellationError()
            }
            print(number)
            print(Date().description)
        }

        request { [weak self] in
            guard let self = self else { return }
            print(self.number)
        }
    }

    override func viewDidAppear(_ animated: Bool) {
        super.viewDidAppear(animated)
        task?.cancel()
    }

    func request(completion: @escaping () -> ()) {
        clouser = completion
    }

    func run() {
        clouser()
    }
}

このViewControllerをmodalで表示するコードを作れば動きを確認できます。
参照ブログ
https://blog.personal-factory.com/2022/08/06/not-require-weak-self-in-task-init/

Simulator.Screen.Recording.-.iPhone.12.-.2022-09-22.at.10.59.48.mp4