There are several issues: 1) sanitary sewer leak, 2) storm sewer leak, 3) watertable issue, 4) sewer pump
First, I’d confirm WHEN it leaks. You’ll need to confirm if it leaks ONLY when you flush the toilet, take a shower, empty the kitchen sink, etc. ...OR... does it leak after a storm, etc.? These are separate pipes with separate issues.
Second, I’d confirm the house has not “moved” (settle) because an underground house has some unique stresses on it and cracks and leaks are early signs of trouble.
1) All plumbing fixtures are suppose to be connected to the sanitary sewer line. You can verify if it’s leaking by flushing dye through the pipes from various locations.
2) To locate storm water leaks, we don’t use dye because it can get messy. Rather, we turn garden hose on and try to make various items leak. You don’t have gutters (underground house) but you could flush catch basins, interior floor drains, etc.
3) I’d keep a journal and make notes as to when the leaks occur and when it’s worse. Subterranean water can rise up during heavy rains. If this occurs, perimeter drains will need to be installed to lower the water table.
4) I’d check to see if your house has a sewer pump. If you are located below the road, then you’re probably below the city’s sewer system (pipes) too.