How to save this Persian silk tree

I moved in December and it has only just flowered where it has foliage. The rest of its branches are dry wood that can be snapped off by hand. There are some cracks in the trunk. I see a few ants and birds eating ants. It wants to live cause it’s putting up shoots from anywhere it can including around its base. The trouble could be that it’s in a little gully that receives the neighbours surface water whenever it rains. Could it be rotting roots with the increased weather events we are getting - my soils is 2 feet of sandy well draining soil and then wet muddy clay. I’m not a fan of non-natives but this would provide glorious shade on the lawn if I can save it. Any suggestions?