The logo is blurry because it’s a pretty small image (169×39) and on your retina screen it’s actually using twice the (physical) pixels to display it (338×78), so it will be resized - scaled UP, in this case.
You should use a much larger image in the first place, use that as a background image for the navbar header, and set it to size 100% x 100% so that it will scale DOWN, which will give you much better quality.
You can create a logo from here https://hatchful.shopify.com/