Apartment with no grounding/earthing... do I really need it?
It is a question of risk level.

People in the USA have lived with ungrounded circuits for decades. With care and proper maintenance you might reasonably expect to live with them without incident.

In other parts of the world, grounded circuits have been the rule for more than half a century.

There is a reason that grounded circuits are now required. That reason is mostly sufficiently large numbers of dead bodies or badly injured and incapacitated living ones.

An approved work-around in the USA is the fitting of GFCI outlets, which reduce the risk of fatal electric shock. But check local code.