FFmpeg can do this.
For example:
ffmpeg -f v4l2 -thread_queue_size 1024 -i /dev/video0 -f pulse -thread_queue_size 1024 -i alsa_input.usb-MACROSIL_AV_TO_USB2.0-02.multichannel-input -vcodec libx264 -vf format=yuv420p -vprofile high -vlevel 4.2 -preset medium -crf 28 -s 720x480 -aspect 4:3 -acodec aac -b:a 128k -channels 2 -ar 44100 "MyDigitizedVideo.mp4"
I will say that I prefer MKV over MP4.
The difference is you need to change the name of your source inputs, especially the name of the audio input.
In the above example, my capture device’s audio input is named alsa_input.usb-MACROSIL_AV_TO_USB2.0-02.multichannel-input
You can also change the -preset to fast if needed.
EDIT: On second read, what do you mean “not play and record”? VHS is analog. There is no such thing as a direct digital copy. You have to play the tape as it is being captured and encoded in real-time.