I eventually found some answer to my question at https://qtcentre.org/threads/21332-ItemIsUserCheckable-and-checking-all-selected-items. Here are some considerations at this topic:

• If extended selection is used in QListView, and items are user-checkable, then pressing "Space" leads to checking of the last selected item. This is no bug, and it works this way for QListView and QListWidget for both Qt and PySide;
• I found no simple way to change this behavior (setEditTriggers() does not affect it);
• As mentioned by @musicamante, there is no simple way to trace, which method called setData() in that case.

Solution

1. If you work in PySide6-designer (or Qt Creator), select "Promote to..." option for QListView and create transformed class, which inherits from QListView (otherwise, just create your custom class, which inherits from QListView),
2. Reimplement keyPressEvent() method there. E. g., following way:

  def keyPressEvent(self, event: QKeyEvent):
    if event.key() == Qt.Key.Key_Space:
      self._checkAllSelected()
    else:
      super().keyPressEvent(event)

Here _checkAllSelected() is new function, which would handle checking of items. I implemented it following way:

  def _checkAllSelected(self):
    model = self.model()
    indexes = self.selectedIndexes()
    setCheckState = Qt.CheckState.Unchecked
    for index in indexes:
      if model.data(index, Qt.ItemDataRole.CheckStateRole) == Qt.CheckState.Unchecked:
        setCheckState = Qt.CheckState.Checked
        break
    for index in indexes:
      model.setData(index, setCheckState.value, Qt.ItemDataRole.CheckStateRole)

Now checking of items in case of multiple selection can be managed.