The classic chemical dissolver is Alum, specifically Potassium Aluminium Sulphate, as sold by Amazon here. Plenty of other sources.
Watch out when ordering. Other chemicals are called “Alum”, and they are more-or-less unsuitable compared with Potassium Aluminium Sulphate. Ammonium Alum Aluminium Sulphate and the others are a waste of money.
Make up a strong solution and fill the hole with it. Leave for several hours, possibly a couple of days. All being well the tap will slowly disintegrate.
Potassium Aluminium Sulphate does not attack Aluminium, Brass or Bronze. Can be used on steel, but it attacks the part as well as the tap, possibly causing unacceptable damage. Keep an eye on it. Not a problem if there’s enough meat to clean out and rethread next size up, but…
If Alum is too corrosive, EDM or a mechanical method. I once removed a broken tap with three piano wires passed through a rod, something like this.

Though it worked, more luck than judgement!
Dave