How can I simplify a long if-else chain when setting JComboBox models based on enum categories?

Separate your concerns.

1. You have a String and want to know which enum it corresponds to.
2. You (now) have an enum, and want to extract its values and pass them along.

For #1, I would do something like this.

    final Class<?> clazz =
        switch (value)
        {

            case "LENGTH"      -> Length.class;
            case "WEIGHT"      -> Weight.class;
            case "TEMPERATURE" -> Temperature.class;
            case "TIME"        -> Time.class;
            case "VOLUME"      -> Volume.class;
            case "AREA"        -> Area.class;
            case "SPEED"       -> Speed.class;
            case "ENERGY"      -> Energy.class;
            default            -> null;

        }
        ;

Ok, now you have a switch expression that takes in a String and then gives you a Class for an enum.

Ok, now let's do #2 and turn that Class into the array of values. This is also easy.

//we have the variable clazz from above
if (clazz != null)
{
    view.getInputBoxUnit().setModel(new DefaultComboBoxModel<>(clazz.getEnumConstants()));
    view.getOutputBoxUnit().setModel(new DefaultComboBoxModel<>(clazz.getEnumConstants()));
}

Note -- the method clazz.getEnumConstants() returns the exact same thing as calling values() would for the enum that the variable clazz is pointing to. Read more here -- https://docs.oracle.com/en/java/javase/24/docs/api/java.base/java/lang/Class.html#getEnumConstants()

Here is the finished product.

private void selectUnit(ActionEvent e) {

    final String value = view.getCategoryBox().getSelectedItem().toString();

    final Class<?> clazz =
        switch (value)
        {

            case "LENGTH"      -> Length.class;
            case "WEIGHT"      -> Weight.class;
            case "TEMPERATURE" -> Temperature.class;
            case "TIME"        -> Time.class;
            case "VOLUME"      -> Volume.class;
            case "AREA"        -> Area.class;
            case "SPEED"       -> Speed.class;
            case "ENERGY"      -> Energy.class;
            default            -> null;

        }
        ;

    if (clazz != null)
    {
        view.getInputBoxUnit().setModel(new DefaultComboBoxModel<>(clazz.getEnumConstants()));
        view.getOutputBoxUnit().setModel(new DefaultComboBoxModel<>(clazz.getEnumConstants()));
    }

}

You might want to use something like this:

  // this method avoids having to rewrite the calls to two "setModel()"
private void set( Unit units ) {
   view.getInputBoxUnit().setModel( new DefaultComboBoxModel<>( units.values() ));
   view.getOutputBoxUnit().setModel( new DefaultComboBoxModel<>( units.values() ));
}

private void selectUnit( ActionEvent e ) {

     // we replace the *if* with a *switch*.
   switch( view.getCategoryBox().getSelectedItem().toString() ) {
      case "LENGTH": 
         set( Length );         break;
      case "WEIGHT": 
         set( WEIGHT );         break;
      case "TEMPERATURE": 
         set( TEMPERATURE );    break;
      case "TIME": 
         set( TIME );           break;
      case "VOLUME": 
         set( VOLUME );         break;
      case "AREA": 
         set( AREA );           break;
      case "SPEED": 
         set( SPEED );          break;
      case "ENERGY": 
         set( ENERGY );         break;  
   }
}

Another way would be:

  // we create a map
Map<String, Unit> map;

  // add the "Unit" with their respective keys 
void createMap() {
   map = new HashMap<>();
   map.put( "Length", Length );
   map.put( "WEIGHT", WEIGHT );
   map.put( "TEMPERATURE", TEMPERATURE );
   map.put( "TIME", TIME );
   map.put( "VOLUME", VOLUME );
   map.put( "AREA", AREA );
   map.put( "SPEED", SPEED );
   map.put( "ENERGY", ENERGY );
}

  // we call to "set" with the "Unit" obtained from the map
private void selectUnit( ActionEvent e ) {
   set( map.get( view.getCategoryBox().getSelectedItem().toString() );
}

private void set( Unit units ) {
   view.getInputBoxUnit().setModel( new DefaultComboBoxModel<>( units.values() ));
   view.getOutputBoxUnit().setModel( new DefaultComboBoxModel<>( units.values() ));
}