Does this not do what you want?

https://docs.easyeda.com/en/PCB/Route/index.html#Differential-Pair-Routing

That only does the initial routing.

So what is desired is:

1. to be able to initially specify and place differential pair traces as a pair and then;
2. as required during layout, to be able to reroute differential pair traces as a pair and not just one trace at a time.

Correct, the tool does number 1.
For number 2. the + & - nodes need to follow each other whichever is moved and maintain the spacing as the angle changes.

I second Steve's request.  It's a real pain not being able to do so automatically

This would need to have an off switch for tuning track lengths.