I didn’t find any link to the Git repository from the PWA app.
There are links for licenses which lead to the respective repositories: https://baby-journal.app/about
the best way to make it this kind of application trustable would be to have no backend
That doesn't work for my family, the data are shared across two people (potentially more in the future), so there needs to be a backend. This also allows for alternative frontends. And as they say, "make the apps you would want to use."
maybe use a remote storage
Remote storage indeed sounds like an interesting technology, but I'm not keen on rewriting the app at this point. Furthermore I'm using the JSON:API standard which I'm very familiar with which speeds up my development significantly.