I will add bolt removal kits to the above methods, consisting of drill bits, appropriate centering caps (for drilling) and serrated pins which are then inserted into the bolt hole and removed. Such sets are a bit expensive, sometimes they fail, but also often they are the only solution (when the break is deep in the hole and nothing can be welded).
There are also screw extractors / extractors (with a left-hand thread that goes into the screw hole while removing the screw itself).
Drilling a hole in the screw can be a big problem (in many cases, nothing will happen with a hand drill - you need stability and precision of guiding the drill, which is often provided only by a milling machine).
The broken bolts are also removed with a punch (punch in the edge of the bolt, tilt it and break it in the direction of turning it out).
And before removing the broken bolt, you can hit it hard a few times (as if you wanted to stick it inside the hole). Then it happens that a broken and seemingly seized screw can be unscrewed by hand (without any tools).
A thermal shock can be added to such a mechanical shock (several heating-cooling cycles).
Chemical boosters rarely help (probably only psychologically - I sprinkled it, it will surely go easier).
In extremely resistant cases and the hardest materials (hardened steels, nitrided steels), a method unavailable to the average citizen will be burning the broken screw with an EDM machine. Partial or with a new thread bored in the hole.
