You need a plumber which I’m not. Storm water and sewage are too different systems. If a rise in storm water is impacting your sewage then storm water is entering those pipes somehow. Generally this is an illegal stormwater discharge point by you or your neighbours into the sewage pipes. You may also have a broken sewer pipe allowing storm water to enter. My first call would be to the water authority that manages the sewer. Their advice will be free and they may check their pipes.

Could be due to the ORG- overflow relief gully being installed to high and allowing the stormwater to drain into the sewer system and the 100mm house service not coping with the influx of water.

Other things to look at are

- blockages in the sewer system affecting discharge flow.

- back flow from the mains sewer service pushing up into your property and discharging out the next lowest point- usually the shower if the ORG has been installed incorrectly or is capped

To fix check overflow heights-

The ORG should be installed so it sits at least 150 mm lower than the lowest fixture in the house. For example, your shower or toilet. It also needs to be least 75 mm above the ground to prevent stormwater flowing into your ORG.

Also camera the sewer and stormy service. Consider installing a reflux valve in the sewer service.

Camera cost to get checked usually $250, any decent local plumber will be able to locate fault fairly quickly.