Can we give an APK/aab file to a client built by my own android studio and signed using my own signing key to upload to his play console?
Will it cause problems ?
You can give your signed .aab/.APK file which should be signed using the key of a particular play console account. ie, you need to have the key alias and password with the Keystore file of a play console account to publish. Otherwise, it will not publish.
So, whichever client you want to give, just ask for the password of their key with key file and sign .aab/.APK using those passwords only using your android studio.