AppleTV Continue Watching changes the app I watch shows with.

Continue Watching should use the last used app for a show by default. It may choose differently if a show pops up earlier on a network channel than on e.g. the Peacock app (or other subscription content provider app). Unfortunately, Continue Watching is easily confused by release timing (and also by episode numbering differences). Note that often network channels are deliberately getting new episodes earlier than VOD services, so you may see a new episode in Continue Watching, before your favorite VOD app has this.

When you manually go into the content provider app and watch an episode there instead, then Continue Watching should be updated with the correct link. If it doesn’t, then remove the episode from Continue Watching, and retry through the content provider app, to have it added again, but this time with the correct link.

Please give feedback to Apple about wanting a more resilient link to the intended third party app, for the Continue Watching queue list. Feedback - Apple TV App - Apple