I would use a separate playback device for the backing tracks, a second computer or iPad with the backing tracks pre loaded.
The use a small 4-channel mixer with the backing tracks and the saxophone and vocal mics routed through it so you don't have to worry about latency coming through the broadcasting software (Zoom, Skype, OBS, Facebook/ Youtube Live, etc...). The output of the mixer connects directly to the audio interface for the broadcast software computer.
And I would strongly urge you to use a real camera for the webcam rather than a built in camera on a laptop or a webcam. Canon and Nikon both make webcam utilities for their DSLR and mirrorless cameras that work very well. You connect the camera to the computer through the USB interface and you don't have to worry about using a separate capture card.
The use a small 4-channel mixer with the backing tracks and the saxophone and vocal mics routed through it so you don't have to worry about latency coming through the broadcasting software (Zoom, Skype, OBS, Facebook/ Youtube Live, etc...). The output of the mixer connects directly to the audio interface for the broadcast software computer.
And I would strongly urge you to use a real camera for the webcam rather than a built in camera on a laptop or a webcam. Canon and Nikon both make webcam utilities for their DSLR and mirrorless cameras that work very well. You connect the camera to the computer through the USB interface and you don't have to worry about using a separate capture card.