Linux

The post explains them quite well. HRIR (Head-Related Impulse Response) and SOFA (Spacially Oriented Format for Acoustics) are standards for representing spacial audio (surround sound) in audio files and streams. A convolver is something that performs convolution (a mathematical term for taking one function, applying it to another, and then producing a third function as a result), and a spatializer is more specifically something that, as the name suggests, gives "space" to audio (distorting audio to represent sounds coming from more than simply 2 directions, or again, what you call surround sound). So HRIR Convolver is simply a method to apply the HRIR function to audio to represent it in a way our brain would interpret as 3D audio, and SOFA Spatializer is simply a method to do the same thing, just with the SOFA standard instead of the HRIR standard. Based on the comments of the post, it seems that they recommend you use SOFA.

In either case, Pipewire supports both standards, and it is trivially easy to implement them through filters (as the post covers in depth). You could try both if you want and see which you prefer. If you're unfamiliar with managing Pipewire and need further resources, the Arch wiki has an entry in great length about it here. I'd recommend reading the comments to that post first if you struggle with anything, such as persistence. Everything you need to set it up should be accessible in that post and its comments.

I'd also like to recommend that you read the post and comments to the post, or simply use a search engine if you come across unfamiliar terms. You can find answers to all the questions you've asked through the linked post and a simple search.