Just going from the words, you have an adapter that provides a stereo headphone connection and a mono microphone connection suitable for a computer headset or stand-alone computer microphone.
I use an ICUSBAUDIO from Startech to do the same thing.
Neither of these has a place to connect a high-volume stereo audio cable for recording.
I use a Behringer UCA-202 to record my stereo sound mixer. It’s a bi-directionial stereo USB interface of good quality and low cost. It’s certified for Audacity overdubbing/sound-on-sound because of its zero latency headphone connection.
We reviewed other similar interface devices.
https://forum.audacityteam.org/t/sound-card-reviews/8375/1
Koz