Programming often makes you feel powerful and in control. Humans love that feeling and it’s intoxicating. But I think that feeling of power and control gets easily conflated with being right all the time. If we’re wrong then it’s like we have to admit we’re not in control anymore.
Source: my ass / own opinion
If the content is being downloaded then you could do the following:
Setup a proxy like Fiddler2 on a PC on the same network your phone is connected to. You’ll need to configure Fiddler2 to decrypt HTTPS and then access the proxy certificate on your iPhone and add it as a trusted certificate. You’ll need to Google how to do this with Fiddler2 but it’s not hard
Configure your iPhone to connect through the Fiddler2 proxy by modifying your WiFi settings. If your PC is allowing connections to the Fiddler2 proxy port (e.g. 8888) and you’re trusted the cert on your iPhone, then connecting to websites in safari should be working
Open the naturespace app on your iPhone and delete the sounds you’re interested in. ONLY do this if you’re sure you can still re-download them. If not, this whole approach won’t work so just stop here.
Download the sounds again
You should then be able to see the web requests that were made to download the sounds in Fiddler2 on your PC. As long as there’s no fancy encryption, you should be able to just save the content out of Fiddler2.