I use Adobe Premiere, its fairly complicated but youtube helps with tutorials. I also use other tools for recording. I use Movavi, but I don't really like their video editor that much. I mainly use them for screen recording and webcam recording. Then I also run Studio One to record the audio. I don't recommend that as it's pro studio audio recording software, but I am a musician and I recorded with it already so I already had the mics, audio interface and software.... I am looking for a way to record screen, webcam (with its audio) and my separate mic audio all in one program, but I have not found it yet. I need the audio from the webcam, so I can sync the good mic's recording with the webcam video. Having the mic in the webcam record also, allows me to sync easily. Hope that all made sense.
What you want to do is a common problem for recording. I use some workarounds with OBS to achieve it, basically edit the canvas size to 3840x1080, then you can place and record 2 by 1080p inputs next to each other. The raw video comes out like this:
Then you use your video editor to duplicate the video then zoom and crop into 2 separate screens on webcam and screen capture. It's not ideal, but the only other option is running multiple instances of OBS, which just adds more complication.
For the audio, you can split everything out into "tracks", which will load into the video editor and allow you to control volume on each track individually, not need to mess with syncing as they were all recorded at the same time. The recording will open up like this if the tracks are setup correctly:
The only thing would be to see if Studio One can feed into OBS, or bypass Studio One completely.
EDIT: To the OP, I been using Davinci Resolve Studio. Happy enough with the software to buy the paid version. The free version is quite sufficient for most tasks those, but a lot of the graphics card performance is only unlocked in the paid version.