Personally I use the mod called Construction Drones (https://mods.factorio.com/mod/Updated_Construction_Drones) but it lacks the integration with Closest First feature (or at least I was unable to config it).

I will look into it

Updated the link to factorio v2 fork

I have looked at the mod! I dont know how much experience you have in modding factorio. One problem is the fact that my mod works only by scaling the personal roboport range to limit what the robots can see. This other mod does not use any preexisting robot implementation. Also no personal roboports. So the only way to implement that they build closest first is to fork the mod and add it in the logic. If i find time i can check how much work that would be and publish a forked version for you

So the integration with Closest First should be inside Construction Drones mod ?
I think I can write that mod author too.

Yes. I thing 90% of all factorio mods use this structure:
You want a new granade? A new vehicle? A new assembly machine or a new faster belt?

All you have to do is, make a deepcopy of an EXISTING “prototype (that are the classes that the devs make for us to use)
For example capsule(granade), vehicle, assembly-maschine or conveyor-belt.
We only implement a new version of these classes.
This other mod does not really do that.
I think it takes an empty prototype (so no logic at all) and does it all himselfe. Via events and regular checks searching the area for objects and managing jobrequests for the new type of robots.
So yes we have to implement the logic there because my mod ONLY works with other mods that use the preexisting prototype “personal-roboport”. And as i said this mod does not do that. I can look into it next week