The evergreen is a Yew (Taxus), and we do not see signs of a pest infestation in the photos, though cannot see the leaf undersides clearly enough to rule-out that possibility. The most likely pests of Yew are scale insects, and in particular, the Cottony Camellia Scale. Sooty mold coating foliage underneath where the insects are feeding is the most obvious sign of a scale infestation, as pictured on this page with more information: https://extension.umd.edu/resource/cottony-camellia-scale-shrubs

The webbing is likely due to spiders; as to why there are so many, there are a range of possible reasons, the simplest of which would be that spring is time for hatching of overwintering spider eggs, and spiderlings may not have dispersed very far before starting to make their own webs. Spiders are beneficial and help control garden pests, so we don't recommend their removal. Over time, as individual spiders move further away, are eaten by birds, or die off for other reasons, the webbing amount should weather-off and diminish. Spider mites do make webs, but are only this prominent when populations are very high - high enough to be causing very noticeable damage, which we do not see happening here. Fortunately, such mites are not a common pest for Yew.

Miri