As suggested in docs, the QGIS message bar is usually the best option to show short messages communicating with the user. 

Is it possible to show the QGIS message bar inside a plugin's GUI developed with Qt Designer as shown below? 

QGIS GUI:<br>
[![QGIS interface][1]][1]

Desired plugin GUI:<br>
[![Desired plugin interface][2]][2]

This would simplify interacting with the user when plugin's window is in full screen mode, hiding QGIS main window.

**EDIT** after J. Monticolo's answer.

In order to integrate J. Monticolo's code to an existing plugin, I inserted this in its main's run method:

    def run(self):
            """Run method that performs all the real work"""
    
            # Create the dialog with elements (after translation) and keep reference
            # Only create GUI ONCE in callback, so that it will only load when the plugin is started
            if self.first_start == True:
                self.first_start = False            
                self.my_msg_bar = QgsMessageBar()
                self.dlg.verticalLayout.insertWidget(0, self.my_msg_bar)
                self.my_msg_bar.pushMessage("Welcome", "This plugin is ready at your service.", level=Qgis.Success, duration=-1)

Where `verticalLayout` is an object introduced with Qt Designer:

[![enter image description here][3]][3]

Reference: https://docs.qgis.org/3.16/en/docs/pyqgis_developer_cookbook/communicating.html


  [1]: https://i.sstatic.net/F7ETW.png
  [2]: https://i.sstatic.net/iisak.png
  [3]: https://i.sstatic.net/fvJwt.png