Help with lawn drainage

Recently moved in to this property and every time it rains the backyard lawn mildly floods and stays wet and slippery for nearly a week after rain. There is a drain up the far end of the yard, but it’s pretty useless.

The ground seems to be very dense and mud like, rather than soil. I’m new to this sort of problem and have always had good runoff or soil in previous properties.

What lawn care or drainage options do I have?