Agree that testing the water with the owner is the right place to start.
But be prepared to walk away. We extended and renovated (back to bricks; walls down, steels in; all new electrics, plumbing and windows) in 2020 and the price increases and supply issues put us 30% over our budget. We moved out, in with family, and even so it was one of the most stressful things I've ever chosen to put myself through! :) I'm glad we did it and the house is lovely but we'll be paying off that overspend for the next 3 years...
From what I hear, prices are only increasing further and contractors are hard to find. Jobs are taking longer because of general scarcity - waiting for people and supplies before you can carry on.
There are real safety issues with kids living around a building site - dust being one, especially if your kids have asthma, but also our (then) 2 yo consistently got himself into a pickle on our brief site visits - running towards holes in the floor he hadn't noticed, etc etc.
As well as doing the maths around purchase costs, professional fees, stamp duty, extension/renovation costs VS the potential re-sale value, you also have to cost up stress, mess, and time spent in a half-done house. Try to put a number on what all that means to you, and add that into the equation.
And then speak to the vendor and see what his number is, and work out what to do from there.
Best of luck either way :)