Where do you now find Sample Programs in the new Developer.Apple web site?

If you mean in one place, I'm only aware of Apple's legacy Sample Code library in the Documentation Archive. Perhaps the plan is to wait until after WWDC before going back to a single repository.

Otherwise, Apple claims samples are here, but the dev is either required to drill down and sniff them out case/by case, or, use the same Documentation Archive from there.

Feel free to file an enhancement request via the bug reporter/suggestions link below if a new/updated sample collection is something you'd like to see.

Good luck.

Sample code is now integrated (well, now being integrated, since it seems to be an ongoing process) into the main documentation pages. For example, on this page:

https://developer.apple.com/documentation/sirikit

if you scroll down to the "Shortcuts" section, you'll see a "{ }" icon indicating sample code, with a link to the Soup Chef sample code. In other words, search for what you want to do, and if there's relevant sample code it will be there, if it exists.

As KMT suggested, if you want to see other ways of searching for or listing sample code, file a bug report. 🙂