My yard floods every time it rains after a landscaping company leveled it, what are my options?

Last summer we hired a company to build a patio and level out our backyard. The patio itself is fine but ever since the leveling work was done, water pools across the entire yard after every rain. It takes days to dry out and some spots stay muddy for over a week. My wife added sand to the worst spots and wants to plant a shrub there thinking it will absorb the water but I honestly doubt that's going to fix anything. From what I understand the problem is that the leveling compacted the soil so much that water can't drain through it anymore. And the yard is now basically flat with no slope to move the water anywhere. I've been reading about french drains, regrading to create a slope, and even something called a soakaway pit. But I have no idea which solution actually fits my situation or if I even need all of that. Has anyone dealt with this after having their yard leveled? What actually worked for you? Should I go back to the company that did the work or find someone who specializes in drainage? Any advice would be really appreciated because another rainy season is coming and I don't want to deal with a swamp in my backyard again.