HDMI 5.1 Windows Chromecast Playstation4?

Question

Audio

Good day, comrades!

[HDMI Chromecast]   ─┐
[HDMI Windows]      ─┼──> [HDMI Audio Extractor] ─┬─> TV
[HDMI PlayStation4] ─┘                            └─> Old 5.1 Surround Audio System

Here's the scheme I came up with. Audio Extractor is one of hundreds from aliexpress.
The thing is. Three games on PlayStation 4 work fine in 5.1 (Last Of Us; GTA5 - fairness, tweak required; Wild Hunt). But neither chromecast nor windows want to work in 5.1. Moreover, they work with the PlayStation in any codec (PCM / Bitstream DTS / Bitstream Dolby), but only games, but videos from youtube, for example, do not. Surprisingly, I haven't found a way to force anything like this on Windows (besides audio "quality"). When trying to say that this is still 5.1 Audio Extractor distributes only the left and right channels.
Maybe someone knows what kind of codec is used on the PS4. And is there any point in digging or is it worth thinking about a normal AV receiver (which, for a second, is 25 times more expensive)? It just comes out funny - exactly what is least expected works.
And does it make sense to try to save money and take a similar thing, but with an optical digital input?
Looking forward to why? Well, I have an old 5.1, since the early 2000s home theaters. It is rather weak and any amp makes hardly five-watt speakers hurt. Therefore, outside of its own ecosystem, it works ... But badly. The system itself has long been installed, if you can get by with a little blood by the forces of the Chinese - why not?
However, having opened it (thanks to the comments), there is a certain emulator mode 2.0 -> 5.1. Although this, of course, is not quite right. But saves on purely 2.0 sources.
Also, I have not tried any left drivers, and there is no particular desire.