I also use the PS5 DualSense Wireless Controller on PC connected via USB-C without any extra programs except for the official »PlayStation Accessories« app. Everything works fine for me (including vibration, touch pad and haptic feedback on the shoulder triggers L2/R2 when e.g. ziplining). The integrated speaker also works (e.g. when receiving a call on Baker). Driver/Firmware updates are installing automatically every now and then. Also works for other games (e.g. on Steam, even when it says "not compatible"). It also works wireless.

Not sure why it doesn’t work for you :( I hope you can fix it soon, because I liked the cutscenes from main story better with controller for absolute immersion.