Most editions gloss this over, assuming that - as lords of the land - the PCs just command enough people to do the job. You also need a sufficient number of workers. Going back to the Companion/Cyclopedia era rules I think you'd need an engineer to oversee the work as well, who you can hire using the Skilled Hireling costs from the PHB, unless a PC has a proficiency in something relevant, like Stonemason's tools, or Carpenter's tools, and wants to take on the task. In other editions of D&D you can accelerate building time by throwing more money at the problem, which suggests that you could up the cost to 12k and get it done in a month and a half, if you have enough workers. since they only quote 400 days for a castle! Maybe they just assume that magic is being used? You can then do the same on construction time (60-150 days), which would give you a figure on the order of 70-80 days (call it 2-3 months), although this is the place where the 5E rules seem least plausible. In the case of Phandelver there isn't much left beyond the basements, so it is pretty ruined (and stone may already have been taken to build the town), so it seems reasonable to go for the higher end, and say it might cost 8k to rebuild. I'd choose a figure in between (say 10-12k) and then reduce it based on how ruined the Manor is. The 5E rules suggest that a Lodge costs 2k to build, while an estate + manor is 25k.

5E is horribly light on such construction details, but there are many rules in previous editions of D&D - none of which seem to have any really consistent numbers attached.

Running a business 5e