OK, so let's look at the different sources:
The recipe is written for people who have all kinds of different systems -- from a mash cooler which leaves 2.5 +/- quarts of wort behind when the wort is drained into the boil kettle to an AIO system where there is no such loss to consider. The instructions are very generic since the writer does not have the information to be specific about the process each user will utilize.
The Anvil recommendations are also fairly generic and designed for those people who want an easy go-to to get close to the desired results. Again, this does not have any specific adjustments for individual process such as wort loss to the spent grains. These are clearly written for those users who do not use software or where close enough is good enough.
The Brewfather numbers should represent your particular equipment if you have taken the time to make adjustments for your style of brewing and equipment particulars. If you are using a stock profile, then it represents someone else's work at dialing in their Anvil to get reasonably accurate volume results given the way they brew.
Even people with the same equipment experience, sometimes significant, differences in results. Differences in grind, extraction efficiency, mash/sparge water split, water retention in the grains, boil off rate due to elevation, etc. will all dictate so one extent or another how much water you actually will need.
If I were to get a new Anvil or other brewing unit, I would first trust the software in which I have the control to enable it to reflect my process losses, efficiency, and brewing style before I trusted a generic set of instructions designed to get one "close enough", whatever that means to the person writing the recommendations.
