Just managed to download the MacOS ChatGPT app. A banner appeared just above the search window for me while logged in at
https://chatgpt.com
Clicking "Download" on the banner downloaded ChatGPT_Desktop_public_latest.dmg
which installed easily.
However, it doesn't do too much. It opens a tiny command line or can expand to a full window that looks just like the web version. You can have it take screenshots and interpret them as illustrated here:
If you open the full app, it works just like the updated iOS app with voice commands (just select the 4o model). Took two tries for it to connect.
Once I downloaded it, the banner didn't appear again (should have taken a screenshot). I cannot find another way to access the download.