Your computer should be more than powerful enough
And using a wired connection to a camera is good. I have no idea the quality of the app you are using. I would suggest rebooting iPhone, not starting anything other than desired camera app, and putting into airplane mode.
With problem persisting when using Sony camera, then most likely it is your settings on the Mac
- of course, you should make sure NOTHING is running in the background that isn't required
- your OBS settings are appropriate. For us to take a look, follow the instructions of the pinned post in this forum
OBS Studio creates a log file each time you run it which contains very useful diagnostic information. Without a log file, it's much harder for any support volunteers to figure out problems and your post may be ignored. To upload a log file, go to the Help menu > Log Files > Upload Last Log...
obsproject.com
HOWEVER, an OBS log will NOT show how well your Operating System (macOS) is running, and overall system utilization. Such configuration and monitoring is up to you
Streaming typically requires H.264, a format which AMD is terrible at/about supporting. However, as you are recording, you may be able to record using the newer H.265 and offload the encoding to your AMD GPU?? Sorry, I have no idea if this would actually work, and if possible, what the quality would be nor how to set up OBS to do that. But from other discussions, seems probably doable. I leave you to do the research on this
The purpose of a capture card is to convert the video output of a device into a format that your computer can accept. For example, my DSLR has USB2.0 output (ie low res) or HDMI. A HDMI capture card would take the HDMI video signal from a device and convert it into a USB signal a compute can accept as a video stream input. A capture card is first and foremost a converter (similar to a cable modem)