What's your question? Ask

Your impatiens are possibly afflicted with gray mold (botrytis), which thrives in humid, damp conditions. My other thought was downy mildew, but that usually presents itself on the underside of the leaves, not the top. The article below outlines a plan of care to help deter the mold from growing - be ready to get out your pruning shears with an approved fungicide in hand.

https://www.gardeningknowhow.com/plant-problems/disease/treating-botrytis-blight.htm

What you are likely seeing is 'honeydew,' which indicates a pest problem from either mites or aphids. This sticky, clear substance seems to crystallize when it dries. I would recommend spraying the plant down and then treating it with neem oil, which is safe and very effective against many types of inset pests. Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

I would suspect the culprit to be slugs or snails. Not only will they devour plants quickly, especially bedding plants like impatiens, but they only come out at night, making it more difficult to catch them. You may not even see signs of their ever having been there, with exception to 'snail trail', the slimey, silvery trail they leave behind. These articles will help deter these pests, especially if you decide to replant: https://www.gardeningknowhow.com/plant-problems/pests/organic-snail-control-how-to-control-garden-snails.htm
https://www.gardeningknowhow.com/plant-problems/pests/facts-about-slugs-and-how-to-kill-garden-slugs.htm
https://www.gardeningknowhow.com/composting/ingredients/eggshells-in-the-garden.htm

There could be watering issues, sunlight, or infestations.
Here is an article that will help you pinpoint the issue.

https://www.gardeningknowhow.com/ornamental/flowers/impatiens/impatiens-problems.htm

Impatiens are extremely sensitive to lack of water.
Your description that the soil around the plants looks like mud, tells me the soil is most likely compacted and poorly draining.
The roots of your plants are probably not able to soak up the water or are sitting in to much water.

I would amend the soil in the area of your garden, Soil should be well draining.

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/improving-garden-soil.htm
https://www.gardeningknowhow.com/ornamental/flowers/impatiens/growing-impatiens-flowers.htm

I would venture to guess that either slugs or cutworms are the culprit in question. Neem oil may help with cutworms, as well as most other insect pests. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/facts-about-slugs-and-how-to-kill-garden-slugs.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/get-rid-cutworms.htm
https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm