any elements on the screen that are not within the AGD area window can be made permanent. Just be careful not to insert CLS commands anywhere! Or at least make sure you have a way of retrieving them, for instance storing them in memory and recalling them when you need them.
Try this yourself: save your AGD game code without any BASIC launcher program. Then reset your Spectrum and re-load it taking care of CLEARing the RAM to make room for the game itself. E.g. if your game code starts at 31000 you should first enter CLEAR 30999, so that the RAM from address 31000 on will be made available.
Then load a screen image with the usual LOAD"" SCREEN$ comand.
Finally, with your game in the RAM and the loaded image on the screen, launch the AGD game with RANDOMIZE USR 32000.
You will find, if you did not use any CLS command in the AGD code, that the game will only occupy the portion of the screen related to the action window, while all the rest will remain unchanged.
This way you can design a frame for your game window, and add a status panel for it. Look at this picture from Apulija-13 for an example:
The frame and status panel are not present in the AGD code, they are stored in memory as a compressed image and recalled prior to the game launch.
If you know at least some BASIC, or even some Z80 Assembly language, you can write a loader/management program for your game that will load the picture after the game code - the same way you did with the example above - and then launch the game. Or, even better, you can compress your image with an external utility like LetharGeek Compressor or ZX7, store the compressed screen in the RAM below the AGD code, and recall it before starting your game. But this would require some more proficiency