One part of my immigration process was approved, but another connected part is still pending with no updates, and I’m confused about whether those linked cases normally move on different timelines or if the delay could mean a problem with the remaining application.

That’s actually very common and usually not a problem. Even when applications are connected, USCIS often processes each part on its own timeline, so one piece can be approved while the other just sits waiting in a different queue. The delay doesn’t automatically mean there’s an issue with the remaining case, especially if you haven’t received any requests or notices. In most situations it’s just uneven pacing rather than something being wrong.