For the software in the video you have posted, it helps for me to deactivate the echo cancellation and automatic gain control.
I also missing the capture mode in TS5… how is it possible, that there are many threads with the same topic and nothing happened to solve this problem in TS3 or 5? My linked Threads are from 2012.
Especially Teamspeak, which is popular for the good audio quality should support 24bit/48khz from Audio Interfaces or Mixers without any problems. In other Tools like Audacity or OBS there are no problems.