If the target knows that the adversary is going to keep torturing them until they die, then what incentive do they have to divulge anything?

As soon as the torturer tells you that they don't know how many secrets you have, you can just say "Whelp, guess I'll just die then" and spend the rest of your hopefully-short life wondering why they don't understand that the only motivation you had to speak was the possibility that the torture would stop.

In reality, though, most regimes that would be willing to torture you would do it even if they knew you didn't have any secrets, just to make an example of you to deter your allies, or they wouldn't need the information you had because they could just tell a judge to convict you on falsified evidence, or tell the public that you shot yourself in the back of the head 8 times.

For the few use cases where there is some vital secret that you don't want the government to know, and they are willing to use torture to find it out, you make sure that the secret is encrypted with a key that is split between multiple (mutually unknown) people across multiple jurisdictions, so that there is no harm in divulging your portion of the key the moment you are caught.

First, it assumes that resources is the only dimension here which is incorrect. History is full of failures of well-resourced, and practically unrestrained security services. Second, safety is not a set of just "on", and "off" states. It's a game of probabilities.