How to render stage in a FBO and display it on screen (doesn't work well with screen viewport for now)

FBOStageSSCCE.java

package com.mygdx;

import com.badlogic.gdx.ApplicationAdapter;
import com.badlogic.gdx.Gdx;
import com.badlogic.gdx.backends.lwjgl.LwjglApplication;
import com.badlogic.gdx.backends.lwjgl.LwjglApplicationConfiguration;
import com.badlogic.gdx.graphics.GL20;
import com.badlogic.gdx.graphics.Pixmap.Format;
import com.badlogic.gdx.graphics.Texture.TextureFilter;
import com.badlogic.gdx.graphics.g2d.Batch;
import com.badlogic.gdx.graphics.glutils.FrameBuffer;
import com.badlogic.gdx.scenes.scene2d.Stage;
import com.badlogic.gdx.scenes.scene2d.ui.SelectBox;
import com.badlogic.gdx.scenes.scene2d.ui.Skin;
import com.badlogic.gdx.scenes.scene2d.ui.Table;
import com.badlogic.gdx.utils.viewport.FitViewport;

public class FBOStageSSCCE extends ApplicationAdapter
{
	public static void main (String[] arg) {
		LwjglApplicationConfiguration config = new LwjglApplicationConfiguration();
		config.width = 1024;
		config.height = 768;
		new LwjglApplication(new FBOStageSSCCE(), config);
	}
	
	private Stage stage;
	private FrameBuffer fbo;
	
	/** > 1 for blur/pixelized, < 1 for antialias (over sampling) */
	private float decimate = 2f;
	
	@Override
	public void create() {
		
		stage = new Stage(new FitViewport(Gdx.graphics.getWidth(), Gdx.graphics.getHeight()));
		
		Skin skin = new Skin(Gdx.files.internal("skins/game-skin.json"));
		
		Table root = new Table(skin);
		
		SelectBox<String> sb = new SelectBox<String>(skin);
		sb.setItems("a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t");
		
		root.add(sb);
		
		stage.addActor(root);
		root.setFillParent(true);
		
		Gdx.input.setInputProcessor(stage);
		
		fbo = new FrameBuffer(Format.RGBA8888, (int)(Gdx.graphics.getWidth()/decimate), (int)(Gdx.graphics.getHeight()/decimate), false);
		
		// optional : blur or pixelize
		fbo.getColorBufferTexture().setFilter(TextureFilter.Nearest, TextureFilter.Nearest);
	}
	
	@Override
	public void resize(int width, int height) {
		stage.getViewport().update(width, height, true);
	}
	
	@Override
	public void render() 
	{
		Gdx.gl.glClearColor(0, 0, 0, 0);
		Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT | GL20.GL_DEPTH_BUFFER_BIT);
		
		boolean useFBO = true;
		
		if(useFBO){
			
			stage.getViewport().update(fbo.getWidth(), fbo.getHeight(), true);
			
			fbo.begin();
			
			Gdx.gl.glClearColor(0, 0, 0, 0);
			Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT | GL20.GL_DEPTH_BUFFER_BIT);
			
			stage.act();
			stage.draw();
			
			fbo.end();
			
			stage.getViewport().update(Gdx.graphics.getWidth(), Gdx.graphics.getHeight(), true);
			
			Batch batch = stage.getBatch();
			batch.getProjectionMatrix().setToOrtho2D(0, 0, 1, 1);
			batch.begin();
			batch.draw(fbo.getColorBufferTexture(), 0, 0, 1, 1, 0, 0, 1, 1);
			batch.end();
		}
		else{
			stage.act();
			stage.draw();
		}
		
	}
}