SOD help!!

Live in Houston and I just moved into a new home back in November 2023. From the jump, my new installed SOD in the backyard has remained either a bit wet or muddy in certain areas (depending on rain fall). I get that it would be wet after heavy rainfall but it’s now been 2 months and it’s never been fully dry. I stopped watering it completely and I have seen better days but still not to the point where I can walk back there and not have dirty shoes. Every time my dogs go out there I have to clean their paws as they’re muddy. The water does seem to be draining via the french drain but the SOD remains wet. I do notice the worst of it is in the shade (house covers half of my yard. Weather has ranged between 40-60 degrees and Houston is definitely more on the humid side. Is this something to be concerned about? What should I do?