I’m not sure this is a bug – I think it’s just not supported. Recording audio from a microphone, and internally capturing audio streaming from another app are different things. I suspect that what GoodNotes is doing is a capture, as opposed to using the mic to record sound playing out of the speakers (which would give you terrible sound quality).
However, if you already have access to the audio in a digital form – it would generally be easier to just download, edit (if needed), and attach that directly to your note in AnkiMobile.
I only recently started using GoodNotes for learning a foreign language. The recorded sounds in GoodNotes have some noise, but it’s acceptable to me. It’s not that bad.
Unfortunately, I am using the website https://www.collinsdictionary.com/dictionary/french-english/ to look up words while learning on my iPad. I’m not sure how to get the audio resources or urls on my iPad. It’s easer to get them on a computer (I’m not using a Mac), but synchronizing data across different devices is difficult and not productive.
If you want batch generated TTS, HyperTTS is probably the best for that.
If you want a TTS voice to just read the card when you study (takes up less space, but often requires an internet connection when you study), you can use Anki’s built-in TTS or Hyper TTS.
If you want to download files of native-speaker audio, there might be add-ons you can use, but they will probably be specific to the site you are getting the audio flies from.