At 250°C you'd mostly get roasted (torrefied) wood rather than real biochar, which needs roughly 400°C or more, so it would likely tie up nitrogen in the soil at first, and baking timber in a kitchen oven also gives off smoke and fumes. If you try it, crush it small and mix it into finished compost for a few weeks before it goes near the brassicas. Chimney soot isn't a good substitute and can contain unwanted residues, while a little plain wood ash is fine as a potassium source, but use it sparingly.

If I crush roasted(at 250°C) wood and mix it into finished compost a few weeks before using will it improve the soil in the same way as biochar?

If it is less effective than real biochar, what might the difference in the effects involve?

...I think soot is meant to add nitrogen to the soil.I was unclear whether or not it would improve the consistency You seem to be suggesting it would not have such an effect.

(I burn wood in the chimney,so I doubt there could be an unwelcome residues)

Creosote builds up in chimneys, and is a toxic addition to soil.

@annpat

Ah,I see now that soot is not great even if it is untreated (I imagine pine soot may be even worse as it is full of resin)