Engineering programs do include a required ethics class. But with a cynical lens, it's only required because the bodies that license engineers and permit them to practice require that course in order for a school's degrees to be accredited. Once an engineering graduate is licensed and practicing, they're on the hook to follow a standard of practice that includes ethics. If they violate that, their licensing body has the legal teeth to punish them in a variety of ways (e.g. fines, removing their license). Also, employers who do engineering work have to agree to a similar deal with the licensing body. If they force engineers to act unethically, those engineers can report them to the licensing body who also has the legal teeth to go after them in a variety of ways. It's not a pretty system but it generally does an okay job.

The ethics course itself is a very small piece of the puzzle. Even if every software engineer had to take an ethics course, there's still a huge power imbalance between the average engineer and their employer. Ethics are great and all, but without a legally backed standard of practice to protect those engineers, widespread violations are more or less inevitable. You can stand up and refuse to do work because it goes against what you learned in your ethics class, but your employer can just find someone who doesn't feel as strongly about that. That still happens in traditional engineering fields, but there's at least a legal/regulatory framework in place to discourage it.

Some jurisdictions "solve" this by lumping software engineering in with other disciplines and making the same licensing bodies deal with it. This is also a big mess. Those bodies are normally led by "traditional" engineers who barely understand software, their standards/legislation were written before software-specific issues (e.g. mass surveillance) were relevant, and their processes don't move fast enough to deal with a rapidly changing field like software engineering. It may be possible to fix all this or create similar organizations and legislation specific to software, but it's not trivial.