The EngineerMode app has been removed permanently by Google's request. It won't be available in any new software versions of any Android based smartphones. You can flash an older version with SPFT or you can just simply perform a factory data reset. The EngineerMode was never officially supported, from now it's not even available.
The sound recorder should work without any issue. Try to erase its data. About the GBoard, uninstall all other keyboard apps, then try again. If that doesn't help, you might need to perform a factory data reset.
I had the same problem, gboard stopped and then I could not access it anymore, I disappeared. I tried installing from playstore and it gives me error 505.