I found a solution to the issue where the OpenAI ChatGPT mobile app fails to log in and shows the "PlayIntegrity verification failed" error on Huawei phones running the HarmonyOS system.
This fix applies to all HarmonyOS versions below 4.3.
Official download link for gptAssist from the F-Droid website:
https://f-droid.org/en/packages/org.woheller69.gptassist/