The HT processor box packs so much stuff into one box it is not going to sound great. So, a separate integrated is a better choice. Purpose built for the least number of functions nearly always sounds best.
I am kind of jumping in on this late, but I do have a couple comments. If you want to use your PC to do all sorts of audio/video output (including Atmos and stuff), it's best to keep HDMI output. If you wanted only 2-channel stereo, there are other better alternatives.
That being said, you can improve the quality of the HDMI output from your PC. One way is to upgrade your computer power supply. Put in the largest you can for smoothest current/power - something like Seasonic TX-PRIME 1600. The second item is to upgrade your video card (depending on what you currently have). The newer cards have more power phases for the GPU and output - this translates into a cleaner HDMI signal. I think the minimum I would recommend is a NVIDIA GTX 1650 card.
What is your current power supply and video card?