Honestly I'm using the same method you mentioned to stay up to date, also taking a look at API diffs when new sdk versions are published, and testing beta iOS versions as well when they go out.

Hey ! Our users report similar issues, it's even happening on different categories like "Productivity and Finance", or with particular search in the picker. We opened a bug report for it in august, If you could do the same it would probably help to get more visibility on if from Apple ! You can reference the FB11400221 bug report ID. 100 % agree that the picker in the screentime settings is better ! Don't know if you noticed but the developer accessible one got a search bar since iOS 16.4, and we got several radar fixed as well, so things are moving !