Q: I’m looking for groundcovers that tolerate soggy soil.

A: Several spreading plants grow reasonably well in wet soil. Creeping jenny (Lysimachia nummularia ‘Aurea’), variegated Japanese sedge (Carex morrowii ‘Variegata’), sweet flag (Acorus gramineus ), and bugleweed (Ajuga reptans ) fit the bill.
More plants for damp soil at Flowers for Damp Soil