Strange problem with a portable touchscreen: touch addressed on the wrong screen

This, although happening on a Framework laptop, is not a Framework specific problem. I am just asking for help from fellow users out of desperation.

Problem

I bought a new Verbatim touchscreen and trying to use it on my Fedora 43 Framework laptop. The display works as expected with the USB-C + Thunderbolt connection. Powering up and everything. Except the touch behaves oddly – the touch it register goes to my main screen instead of itself (secondary).

I have set it as an extended monitor. And I intend to use it that way. So I want to fix the touch.

Attempted Fix with gsettings

I tried to set gsettings with steps inspired by the instructions here:

  1. I checked the hardware information of the screen using hwinfo:
    $ hwinfo --monitors
    46: None 00.0: 10002 LCD Monitor
      [Created at monitor.125]
      Unique ID: rdCR.crX5FdnqKe6
      Parent ID: 0Gk3.fV4E8xPcyB4
      Hardware Class: monitor
      Model: “Verbatim MT15”
      Vendor: RTK
      Device: eisa 0x0003 “Verbatim MT15”
      Serial ID: “demoset-1”
      ...
      Config Status: cfg=new, avail=yes, need=no, active=unknown
      Attached to: #21 (VGA compatible controller)
    ...
    ...
    
  2. I then run the following gsettings command:
    $ gsettings set org.gnome.desktop.peripherals.touchscreen:/org/gnome/desktop/peripherals/touchscreens/0457:0819/ output "['RTK', '0x0003', 'demoset-1']"
    

After restart, the problem is still there.

Any advice on what I might try next?

One thing I noticed is that both the main (Framework’s own) and the secondary monitor seem to be connected through the same USB hub (#21):

21: USB 00.0: 10a00 Hub
  [Created at usb.122]
  Unique ID: pBe4.j32TdkAq37E
  SysFS ID: /devices/pci0000:00/0000:00:08.1/0000:c1:00.3/usb2/2-0:1.0
  SysFS BusID: 2-0:1.0
  Hardware Class: hub
  Model: "Linux Foundation 3.0 root hub"
  Hotplug: USB
  Vendor: usb 0x1d6b "Linux Foundation"
  Device: usb 0x0003 "3.0 root hub"
  Revision: "6.17"
  Serial ID: "0000:c1:00.3"
  Driver: "hub"
  Driver Modules: "usbcore"
  Module Alias: "usb:v1D6Bp0003d0617dc09dsc00dp03ic09isc00ip00in00"
  Config Status: cfg=new, avail=yes, need=no, active=unknown

Could that be a factor to my problem here?