Is there any app that can save all of my heath data so that next time I restore I won't have to enter it manually? For example Lark saves my sleep analysis in the cloud and I want something for "Steps" too.
Are you talking about restoring as new?
If so, as of right now I haven't found a way to export Health Data and re-enter it. I know you can export a raw file in Health and it emails it to you, but it can't be reimported as of now. There is an app called "Health Importer" that is working on an update to reimport that exported Health file.
If you are not talking about restoring as new, all health data is saved in iCloud and will be restored when you restore from an iCloud backup.