Spider Web: Hit: The target is restrained by webbing. As an action, the restrained target can make a DC 12 Strength check, bursting the webbing on a success.
So... Can you use your Athletics to escape this like for a Grapple ?
The rules text says Strength and not Athletics and that's probably for a reason. Getting loose from a spider web seems like a feat of pure strength to tear apart the strands of the web, unlike grappling that involves a lot of technique.