Q.How Can I Fix This?
First off, can you identify this shrub? A gold arborvitae? Secondly, the main question, how do I fix this hedge? I recently bought a house that had a volunteer cotoneaster lacteus growing between two shrubs on the right. The previous homeowner trimmed back the evergreen to make room for the cotoneaster. I am in the process of cutting out the cotoneaster since it’s an invasive and it was a terribly pruned eyesore. Is the original hedge salvageable? Or should I just cut down the one on the right? How do I fix it?

Certified GKH Gardening Expert
This reminds me most of Thuja occidentalis, and of a "golden" cultivar, just as you speculate. You might never get it back to its original shape, but cutting the damaged portions out, and treating with a fungicide may help restore its health.
https://www.gardeningknowhow.com/ornamental/trees/arborvitae/growing-emerald-green-arborvitae.htm
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm