Which external USB Soundcard do I need?

That is not what we are talking about here, we are not running windows audio into a DAW, it's simply allowing both the single client ASIO pipeline and the multi-channel Windows shared audio to both output at the same time and there is nothing I have read that warns against this, to the contrary most advise I have seen suggests what I echoed to make sure you have both Windows and your DAW settings set to the same sample/bitrate for this to work otherwise loading a DAW with a different sample rate will place the whole windows audio system offline.

Just found this if it helps. Could be what you're looking for.

https://www.amazon.co.uk/Native-Instruments-Komplete-Two-Channel-Interface/dp/B07N6RD68M/ref%3Dsr_1_5?crid=BRE01IJLFOCR&dib=eyJ2IjoiMSJ9.4PObSotdG4Q2jeuOQ0TSEY-I2pkeY-YuxDaZUHQTsIEsCeIf97Q1cHB29_3qjdaa-sQLubWbGfMBiWQchcG1rf_TYmgonwlrrVx8BxH40B2nUAyuqlS0togjJ2mnUQZNqnGIHA_NHcNWIpFnJiGs0lwFMmLYu2KNM6F9JhHdhkfrdxX2d_wh5R-Grrl54ArHXH4ZLrq_MM1QVKwQgxAd2hcHLma1wnlVIyDBnaBSDxL9kv5w5X1uMZJGxKCf3FmSX9DiYN3vpHBIaNOA3VV2GgakRh76MAmsTUOKJ96H_-c.jYhjyF_uJYuqFpw8MTZQL8EUq_dTu9up-gAmgKsADuQ&dib_tag=se&keywords=native%2Binstruments%2Baudio%2Binterface&qid=1714737869&sprefix=Native%2Binstruments%2Baudio%2Caps%2C95&sr=8-5&th=1

IMO there should be no need to involve a second audio interface, or ASIO or ASIO4ALL.

As long as the audio config is correct, it should be possible to hear audio from both Komplete Kontrol and YouTube at the same time with the onboard audio interface.

I've just tested here and it works fine. Onboard Realtek audio, no latency, both sources audible.

Something is amiss. As requested previously, please post a pic of your audio settings from Komplete Kontrol.

Another audio interface will make no difference if your audio settings in Komplete Kontrol are incorrect.

Using ASIO is more likely to make matters worse, as generally ASIO does not allow sharing.