I was able to solve this issue using @HangarRash's idea with a custom container view and a little bit of constraint math.

import UIKit

class ViewController: UIViewController {

  override func viewDidLoad() {
    super.viewDidLoad()
    // Do any additional setup after loading the view.
    
    let w: CGFloat = 64
    let h: CGFloat = 64

    let v1 = UIView(frame: CGRectMake(0, 0, w, h))
    let v2 = UIView(frame: CGRectMake(0, 0, w, h))
    let v3 = UIView(frame: CGRectMake(0, 0, w, h))
    let v4 = UIView(frame: CGRectMake(0, 0, w, h))
    let v5 = UIView(frame: CGRectMake(0, 0, w, h))
    let v6 = UIView(frame: CGRectMake(0, 0, w, h))

    v1.backgroundColor = .red
    v2.backgroundColor = .green
    v3.backgroundColor = .yellow
    v4.backgroundColor = .gray
    v5.backgroundColor = .cyan
    v6.backgroundColor = .purple
    
    let views: [UIView] = [v1, v2, v3, v4, v5, v6]
    
    let gap: CGFloat = 16
    let width: CGFloat = 32
    let height: CGFloat = 32
    let totalWidth: CGFloat = width * CGFloat(views.count) + gap * CGFloat(views.count-1)
    let container = UIView(frame: CGRectMake(0, 0, totalWidth, height))
    
    container.widthAnchor.constraint(equalToConstant: totalWidth).isActive = true
    
    for (i, view) in views.enumerated() {
        view.translatesAutoresizingMaskIntoConstraints = false
        container.addSubview(view)

        NSLayoutConstraint.activate([
            view.widthAnchor.constraint(equalToConstant: width),
            view.heightAnchor.constraint(equalToConstant: height), // match container
            view.centerYAnchor.constraint(equalTo: container.centerYAnchor),
            view.leadingAnchor.constraint(equalTo: container.leadingAnchor, constant: CGFloat(i) * (width + gap))
        ])
    }
    
    let containerItem = UIBarButtonItem(customView: container)
    if #available(iOS 26.0, *) {
      containerItem.hidesSharedBackground = true
    }

    navigationItem.rightBarButtonItem = containerItem
  }
}

extension UIView {
  func anchor(to size: CGSize) {
    translatesAutoresizingMaskIntoConstraints = false
    let constraints = [
      heightAnchor.constraint(equalToConstant: size.height),
      widthAnchor.constraint(equalToConstant: size.width)
    ]
    for constraint in constraints {
      constraint.priority = UILayoutPriority(rawValue: 1000)
    }
    NSLayoutConstraint.activate(constraints)
  }
}