Syrinscape can play on multiple different devices, so you can run it on whatever you use at your table. PC/Mac, phone or tablet. hook it up to a good set of bluetooth speakers and you are good to go.
If you want to just use a phone or tablet to remote play Syrinscape and have the app running on a more powerful computer you can do that through Syrinscape Online
Is your home theatre system Bluetooth connectable? if so then connect it to whichever device you have running Syrinscape and you are good to go. Connect a tablet or phone to the PC through Syrinscape Online and then you can remotely trigger the sounds and still use your tablet/phone to look at DnD Beyond or any other programs you use at the table
Syrinscape always defaults to whatever audio setting is active when the program loads up. so its detecting stereo when it loads and defaults automatically to that. One of the improvements we are making this year is an easier way to switch between outputs and manually set defaults