Hi. I also had the exact same problem with my PSP (video works, audio doesn't), but I managed to solve it. Unfortunately, I have a different PSP and method of video capturing, so I can't say for sure that my setup works for the PSP Street or Remote Joy plugin. I assume that your cable is the USB mini-to-USB cable because I also rely on a USB connection, so there might be a chance that I can help you.
After tinkering with my working setup, I noticed three factors that affected my audio output.
1. On Windows, go to Settings > Privacy > Microphone > Turn on microphone access
2. Assuming that you have a Video Capture Device in Sources, go to Properties > Audio Output Mode > Capture Audio Only > check "use custom audio device" > Audio Device > Digital Audio Interface (USB Digital Audio)
3. Go to Edit > Advanced Audio Properties > Audio Monitoring (Video Capture Device) > Monitor and Output
Hopefully this helps!
(Windows 10, PSP 2000, PSP 2000/3000 HDMI cable + HDMI-to-USB Video Capture Card)
