Cannot save as JPEG XL (.JXL)

Start at Pinta.Core.GdkPixbufFormat in the Save As flow and inspect how the Flatpak build supplies gdk-pixbuf and JPEG XL support. Reproduce saving an image as JXL in the Flatpak; done means the Flatpak can save JXL without the reported gdk-pixbuf exception.

I am having the same issue as https://github.com/PintaProject/Pinta/issues/1857:

Description
The build of gdk-pixbuf that ships with the Flatpak version does not support saving as JXL.

To Reproduce

1. Draw anything
2. Save it as JXL
3. Get errored

Here is the error I receive:

GLib.GException: This build of gdk-pixbuf does not support saving the image format: jxl
   at GdkPixbuf.Pixbuf.SaveToStreamv(OutputStream stream, String type, String[] optionKeys, String[] optionValues, Cancellable cancellable)
   at Pinta.Core.GdkPixbufFormat.DoSave(Pixbuf pb, File file, String fileType, Window parent)
   at Pinta.Core.GdkPixbufFormat.Export(Document document, File file, Window parent)
   at Pinta.Actions.SaveDocumentImplmentationAction.SaveFile(Document document, File file, FormatDescriptor format, Window parent)
   at Pinta.Actions.SaveDocumentImplmentationAction.SaveFileAs(Document document)
   at Pinta.Actions.SaveDocumentImplmentationAction.Activated(FileActions sender, DocumentSaveEventArgs e)
   at Pinta.Core.AsyncEventHandlerExtensions.InvokeSequential[TSender,TArgs,TResult](Returning`1 handlerBundle, TSender sender, TArgs args)
   at Pinta.Core.FileActions.RaiseSaveDocument(Document document, Boolean saveAs)
   at Pinta.Actions.SaveDocumentAsAction.Activated(Object sender, EventArgs e)
   at System.Threading.Tasks.Task.<>c.<ThrowAsync>b__124_0(Object state)
   at GLib.Internal.MainLoopSynchronizationContext.<>c__DisplayClass1_0.<Post>b__0()

I am using version 3.1.2, running LMDE 7 (Debian 13) on the host. Let me know if you need anything else.

Edit: libjxl0.11 and libjxl-dev are installed on the host system.