They usually only ever snap at one of the ends. If it’s snapped at the carb end then you’ll have noticed it when you inspected the choke butterflies so it’s probably at the lever end where it’s gone. If you whip off the cover around the handbrake lever you’ll see two 10mm bolts holding the lever down. Just undo them and see what the cable looks like there. The other scenario is that the linkage operating the butterflies has broke. On the Weber versions you can see it plainly but on the polish ones it’s not so obvious.