Many code formatters decide whether to use " or ' based on some configuration and whether the default one would require escaping. So if you are using such a code formatter, this is no longer a deliberate choice unless you explicitly override the behavior with annotations.
I am not sure whether your solution of using a less intense color for the unchanged part of the string would make it clearer. It is just more similar to other diff tools that highlight the whole line with a less intense color if it contains changes.