It sounds like the answer to my question "How can I tell what CPUs a cooler is for?" is, "You can't." That's discouraging, although given what I already knew it's not totally surprising.
The precise question I meant to ask was: How to tell what CPU socket a fan is designed to work with? That's how sellers describe their coolers. (Part of this is about the possibility of selling my surplus coolers on eBay.) As far as I know, though, the form factor of the cooler itself is the same for all Intel sockets and all AMD sockets, so that is no help.
You said that coolers have different heat dissipation capacities, which makes them suitable for different types of CPUs. I can look up a given CPU's TDP, but I don't know a way to connect that with the cooler classification by socket type.
At this point it looks like my only option is to assign any unidentified cooler (i.e. almost all of them) to the CPUs with the lowest TDPs -- except that I don't even know what CPUs those are.
If you or someone else can shed even a little more light on this matter -- secret knowledge, rules of thumb, special case solutions -- it will be welcome.
While typing this message I noticed that "CPU cooler" and "CPU cooker" differ by only one letter, both in the alphabet and on the QWERTY keyboard. It's an appropriate coincidence.