When visiting chatgpt.com, no favicon is displayed in the tab:

Also, when adding that website to the bookmarks bar, a generic favicon is used:

The chatgpt.com HTML has these (and the URL's are all valid):
<link rel="icon" href="https://cdn.oaistatic.com/assets/favicon-eex17e9e.ico" sizes="32x32"/>
<link rel="icon" href="https://cdn.oaistatic.com/assets/favicon-l4nq08hd.svg" type="image/svg+xml"/>
<link rel="icon" href="https://cdn.oaistatic.com/assets/favicon-l4nq08hd.svg" type="image/svg+xml" media="(prefers-color-scheme: dark)"/>
In the Network tab, I can see Orion RC downloaded these files:

They show in sources as well:

For comparison, on Safari 18.6, it doesn't show the favicon in the tab either but when I drag the URL to the bookmarks bar, the bookmark does have the correct favicon (and the open tab immediately updates with the icon too).
Version 0.99.135.0.1-rc (WebKit 622.1.15.19.2)
Build date July 30, 2025
Mac 15.6 (Build 24G84)
The favicon would be displayed in the open tab as well as in the bookmarks bar.
0.99.135.0.1-rc
Sequoia (15)