It took a little bit of tinkering for me, but it appears there was some CSS in the index.html file that was modifying the sidebar and making the "New Chat" button not appear.

1. Go to the file at this location:

~/Applications/ChatGPT.app/Contents/Resources/app/index.html

2. Delete lines 17 - 43 (The entirety of the function webview.insertCSS)

Index.html should now look like this:

3. Save the file once those lines are deleted. Reload the application and the “New Chat” button should be there :)

sweeeet, thank you
not sure why I didn't think to just try to edit the app contents