OP growing up my parents had a big woodburner in the sitting room which had a back plate boiler. It heated the hot water for baths etc and also for the radiators. The sitting room was always like an oven but the rest of the house was bloody freezing; to get enough heat so the rads would get warm, you need to have the fire roaring! It’s definitely not ideal.
They also had an electric immersion so in the summer you could just put the immersion on for an hour which heated hot water for baths, but no radiators. There was also an electric towel rail in the bathroom to air bath towels, and a tumble dryer for drying/ airing clothes in the summer.
Interestingly, they have in the last couple of years moved to a similar sized house which has mains gas heating and their overall heating/ electric costs have gone down. I think that was the electric immersion, tumble drying and electric towel rail bumping things up.
OP don’t underestimate the work involved with log-fired anything. It takes bloody ages to stack logs, and it’s back breaking. My dad used to carry down a large bag of logs every day which they’d get through to get the house warm. It would have taken me two trips to bring in the same amount of wood - and you have to do that every day.
In our house which we have woodburners as well as central heating, we get through a fraction of the wood, but then ours isn’t driving a back plate boiler..