Well, call it patina!
Wot Bazyle said.
And, electrolysis in Caustic Soda solution is very effective on larger lumps of steel.
For delicate items more than one approach may be needed. Take the Jacobs chuck as an example. Outside it’s robust, but inside there are somewhat delicate sliding parts and springs. Rough treatment could ruin it, assuming it’s not beyond repair already. Items like that often have to be stripped down, which may require a long soak in penetrating oil, and strong heat just to get them apart.
May not be worth it. The tapers have physical damage, which is bad. Tapers rely being in good condition to get a tight grip, so I’d rather replace a battered one than take the risk. If a manky male taper lets go and spins it’s likely to damage the socket. Also, if the teeth are damaged, the key will slip, which is a nuisance.
The rust on the HSS tools is cosmetic, so a quick swipe with a wire brush would be more than enough for me.
Unless you want the practice – a very valid reason – look carefully at old tools before spending time on them. For example, the centre-drill has a broken end, and a new one is only a few pounds.
The idea that old tools are marvellous compared with modern rubbish is common on the forum, but I have my doubts. Those chucks were good when they were new, but have obviously been neglected, possibly because they were worn out in 1958 and put in a box. What happens to tools in the decades after they were sold makes all the difference, and many old tools, no matter how well-made originally, are in poor condition.
The way to find out how good those chucks are is to strip them down, clean, reassemble and test in a drill. It’s very educational. If they’re OK, then de-rust the outside and make them beautiful again. Otherwise you may start by polishing a turd!
I prefer making things, and would rather buy new than spend a lot of time refurbishing. That’s just me though, for many others the hobby is all about making good and there’s huge satisfaction in bringing old gear back to life.
Dave