So, of those 4 browsers listed in your screenshot of Supported Browsers, which one do you think StreamFab is using? Since you posted the "About" screenshot I'm guessing that you think it is Microsoft Edge 118. The correct answer is none of those. The browser StreamFab uses is Chromium Embedded Framework (CEF) 102. Technically they actually use QCEF which is CEF incorporated into a Qt framework but it is still 102. The reason they use 102 is because if they go above 109 StreamFab would not be able to be used by Windows 7/8/8.1 users and they are still a fair percentage of SF's userbase. Now, on the other hand, websites would prefer you to use the very latest versions of the supported browsers that are available. For that, StreamFab pulls a little trick called a User Agent Switcher which makes the browser look like Chrome 115 run on a Windows 10 computer. As is usual, the cat and mouse games go on, and some websites are using a new method to find out what browser you are actually using which is called User Agent Client Hints (or some variation of that name). This allows them to see that you are actually running the unsupported CEF browser and you get kicked out with an error screen.
Solution? I haven't done much reading on this and I am not a programmer but they might be able to switch away to another browser framework such as Electron or NW.js which have become more accepted. I highly doubt the developer would want to, basically, rewrite StreamFab all over again which is what it would entail.
