POC implementation, using UIListContentConfiguration with UICollectionView to define UI

NavigationDropdownMenu.swift

import UIKit

protocol DropdownMenuItem {
    var appearance: UIListContentConfiguration { get }
}

protocol DropdownMenuSection {
    associatedtype Item: DropdownMenuItem

    var appearance: UIListContentConfiguration? { get }
    var items: [Item] { get }
}

class NavigationDropdownMenu<Section: DropdownMenuSection>: NSObject, UICollectionViewDataSource, UICollectionViewDelegate {
    var sections: [Section] = [] {
        didSet {
            collectionView.reloadData()
        }
    }

    var isShowing: Bool { collectionView.superview != nil }

    private var collectionView: UICollectionView!

    private var cellRegistration: UICollectionView.CellRegistration<UICollectionViewListCell, UIListContentConfiguration>!

    override init() {
        super.init()

        generateMenu()
    }

    private func generateMenu() {
        let layoutConfig = UICollectionLayoutListConfiguration(appearance: .plain)
        let layout = UICollectionViewCompositionalLayout.list(using: layoutConfig)
        collectionView = UICollectionView(frame: .zero, collectionViewLayout: layout)
        collectionView.dataSource = self
        collectionView.delegate = self

        cellRegistration = .init { cell, indexPath, itemIdentifier in
            cell.contentConfiguration = itemIdentifier
        }
    }

    func show(in vc: UIViewController, animated: Bool = true) {
        vc.view.addSubview(collectionView)

        collectionView.translatesAutoresizingMaskIntoConstraints = false

        let fixHeightConstraint = collectionView.heightAnchor.constraint(equalToConstant: 10)
        fixHeightConstraint.priority = .defaultLow
        let heightRatioConstraint = collectionView.heightAnchor.constraint(lessThanOrEqualTo: vc.view.safeAreaLayoutGuide.heightAnchor, multiplier: 0.6)
        heightRatioConstraint.priority = .required

        NSLayoutConstraint.activate([
            collectionView.topAnchor.constraint(equalTo: vc.view.safeAreaLayoutGuide.topAnchor),
            collectionView.leadingAnchor.constraint(equalTo: vc.view.leadingAnchor),
            collectionView.trailingAnchor.constraint(equalTo: vc.view.trailingAnchor),
            fixHeightConstraint,
            heightRatioConstraint,
        ])

        DispatchQueue.main.async { [weak self] in
            // now collectionView is laid out
            if let height = self?.collectionView.collectionViewLayout.collectionViewContentSize.height {
                fixHeightConstraint.constant = height
            }

            if animated {
                self?.collectionView.transform = .init(translationX: 0, y: -20)
                self?.collectionView.alpha = 0.01 // has to be non 0

                UIView.animate(withDuration: 0.3) {
                    self?.collectionView.transform = .identity
                    self?.collectionView.alpha = 1
                }
            }
        }
    }

    func hide(animated: Bool = true) {
        if !animated {
            collectionView.removeFromSuperview()
        } else {
            UIView.animate(withDuration: 0.3) { [weak self] in
                self?.collectionView.alpha = 0
                self?.collectionView.transform = .init(translationX: 0, y: -20)
            } completion: { [weak self] _ in
                self?.collectionView.removeFromSuperview()
                self?.collectionView.alpha = 1
                self?.collectionView.transform = .identity
            }
        }
    }

    // MARK: - UICollectionViewDataSource

    func numberOfSections(in collectionView: UICollectionView) -> Int {
        return sections.count
    }

    func collectionView(_ collectionView: UICollectionView, numberOfItemsInSection section: Int) -> Int {
        let itemsCount = sections[section].items.count
        return sections[section].appearance == nil ? itemsCount : itemsCount + 1
    }

    func collectionView(_ collectionView: UICollectionView, cellForItemAt indexPath: IndexPath) -> UICollectionViewCell {
        let item: UIListContentConfiguration

        if let header = sections[indexPath.section].appearance {
            if indexPath.item == 0 {
                item = header
            } else {
                item = sections[indexPath.section].items[indexPath.item - 1].appearance
            }
        } else {
            item = sections[indexPath.section].items[indexPath.item].appearance
        }

        let cell = collectionView.dequeueConfiguredReusableCell(using: cellRegistration, for: indexPath, item: item)

        if indexPath.item == 0, sections[indexPath.section].appearance != nil {
            cell.backgroundConfiguration = .clear()
        }

        return cell
    }

    // MARK: - UICollectionViewDelegate

    func collectionView(_ collectionView: UICollectionView, shouldSelectItemAt indexPath: IndexPath) -> Bool {
        if indexPath.item == 0, sections[indexPath.section].appearance != nil {
            return false
        } else {
            return true
        }
    }

    func collectionView(_ collectionView: UICollectionView, didSelectItemAt indexPath: IndexPath) {
        let selectedItem: Section.Item
        if sections[indexPath.section].appearance != nil {
            selectedItem = sections[indexPath.section].items[indexPath.item - 1]
        } else {
            selectedItem = sections[indexPath.section].items[indexPath.item]
        }
        print(selectedItem)
        hide()
        collectionView.deselectItem(at: indexPath, animated: false)
    }
}

struct TestSection: DropdownMenuSection {
    let index: Int

    var appearance: UIListContentConfiguration? {
        var configuration = UIListContentConfiguration.cell()
        configuration.image = UIImage(systemName: "heart")
        configuration.text = "Header \(index)"
        configuration.secondaryText = "Secondary Header Text"
        return configuration
    }

    var items: [TestItem]
}

struct TestItem: DropdownMenuItem {
    let index: Int

    var appearance: UIListContentConfiguration {
        var configuration = UIListContentConfiguration.cell()
        configuration.text = "Item \(index)"
        return configuration
    }
}

class ViewController: UIViewController {
    var menu: NavigationDropdownMenu<TestSection>!

    override func viewDidLoad() {
        super.viewDidLoad()

        view.backgroundColor = .systemBackground

        let button = UIButton(type: .system)
        button.setTitle("BUTTON", for: .normal)
        button.addTarget(self, action: #selector(didTapButton), for: .primaryActionTriggered)
        navigationItem.titleView = button

        menu = .init()
        menu.sections = [
            TestSection(
                index: 0,
                items: [
                    .init(index: 1),
                ]
            ),
            TestSection(
                index: 1,
                items: [
                    .init(index: 0),
                    .init(index: 1),
                    .init(index: 3),
                    .init(index: 5),
                    .init(index: 7),
                ]
            )
        ]
    }

    @objc private func didTapButton() {
        if menu.isShowing {
            menu.hide()
        } else {
            menu.show(in: self)
        }
    }
}