If you have a crack in the bowl, you should be able to find water leaking out onto the floor…somewhere. If it’s not apparent from above, check below the floor if you have access.
Back-siphonage of water from the bowl to the drain has been known to occur in poorly or unvented systems, but it is extremely rare and almost always restricted to multilevel buildings.
A more common, but overlooked, problem that causes bowl siphonage is the presence of some sort of partial obstruction in the bowl trap, especially something like cloth or tissue that “wicks” water from the bowl down into the drain line. The first thing I’d recommend is therefore snaking the bowl with a closet auger…