They're probably targeting communications, like those diplomatic cables Manning leaked. I'd assume top secret "design secrets" aren't transmitted. My understanding of spying is it's typically focused on gleaning information from sources a laymen would consider boring and/or useless. For instance, the NSA worked until 1980 to decrypt certain Soviet messages sent between 1942 and 1945 that re-used one-time pad pages:
I don't think that's quite accurate. The Wikipedia article makes it sounds like the issue was more that they didn't want to give their adversary access to their encryption technology. In this context, OTP has the advantage of being both secure and not secret.
https://en.wikipedia.org/wiki/One-time_pad#Historical_uses
> The hotline between Moscow and Washington D.C., established in 1963 after the 1962 Cuban Missile Crisis, used teleprinters protected by a commercial one-time tape system. Each country prepared the keying tapes used to encode its messages and delivered them via their embassy in the other country. A unique advantage of the OTP in this case was that neither country had to reveal more sensitive encryption methods to the other.
Others could be more traditional, like a dragnet that infiltrates common applications or exploits, then hunts for IAM credentials or a DB server.
Users checking tokens with public endpoints into repositories is also very common.
Also, the term is post-quantum cryptography. I don't think it can be declared quantum-safe or quantum-proof just yet.