I think you've pretty much got it. I doubt we can really gleam the true nature of the camps/work training centres but it's pretty obvious that it is not as bad as the media claims while (some of it) may be considered a human rights violation. A large part of their motivation for running these programs is as already mentioned, curbing separatist and terrorist movements but almost more importantly, Xinjiang is placed right within the Belt and Road Initiative (BRI). So the program will involve development into the region as well as work training. I wouldn't be surprised if there are also more extreme measures taken for people they deem as higher risk. One way I like to think about it is by comparing it to the One Child Policy. The motivation for their program isn't necessarily malevolent or genocidal, but they aren't going to place a high value on some individual freedoms.

Some things that may provide some further context is that (1) China actually has quite extensive affirmative action programs for ethnic minorities. For example, minority regions don't have to pay tax to the central government, so that the money can be spent on development. There are also immense education benefits, to the point that some Han Chinese (half) joke about wanting to marry an ethnic minority so their children can get the benefits. (2) Since the time of Hu Jintao's leadership, they have significantly stressed that development was the key to maintaining a "harmonious society". I pretty much see the current programs as a continuation of that.