Two bug infestations
The webs in your groundcover are spider webs. Spiders are beneficial insects that feed on pest insects. They do not need to be controlled.
The browning may be due to poor drainage, lack of sunlight, past winter injury, voles, etc. Prune dead areas and make sure the soil drains well.
Barberry - can be susceptible to several insect and disease pests. We cannot say for sure what you are dealing with from the photos. It also can decline with age. Make sure the soil drains well. Mulch should be no thicker than several inches and away from the base of the stems. Prune dead branches and see if the plant puts out new growth next spring.
Also, here is some information on barberry. This is an invasive plant that displaces native plants and forms thickets in woodlands and other habitats. Its dense foliage creates an ideal humid environment for black-legged ticks (deer ticks) which can carry the pathogen that causes Lyme disease. Here is more about barberry https://extension.umd.edu/hgic/topics/japanese-barberry
If the plants do not put out new growth, then you may want to take the opportunity to replace with some native plants. Match the plants to the site's growing conditions and plan for mature height and width. There are some replacement recommendations on the above link.