Your plant doesn't look overwatered. If your succulent plant leaves are mushy, thats a sign of too much water and should stop watering. Plastic containers shouldn't be a problem, just make sure it has good drainage, you can also try and aerate the soil if the soil is compacted.
You should keep your plant in a dry area, stop watering, and look at the root system for any rot damage. Remove affected leaves, and only keep healthy ones. only re-pot if fungal infection is suspected.
