I removed field bindweed by digging (I had to anyway for various reasons) which pulled out tens of metres of root if not more, then over several years pulling it out whenever shoots appeared. It has now gone. But it had huge amounts of root and can survive years of being pulled out. Composting suppresses most weeds, making it easy to spot the bindweed.
As for horsetail, I have read that growing turnip helps, but having never had it, I don’t really know!