I have created such service a while ago for mainly my own sake. The name of the economy overview website is Keizai and it's far from done. The share feature is a little buggy and an update fixing this will come soon.
PWA is supported. You can self-host Keizai if you want. You own your data and the encryption keys. You can export and import your data and also delete your data or your account at any time. Budget, sharing stuff, and more. More features on the way.
The source code can be found at https://codeberg.org/airikr/Keizai
Native app will maybe come some time in the future. I have zero knowledge of Flutter or any other Android/iOS app languages or what they now are called ๐ We'll see if the native app even will be released since PWA are good enough.
Update 2023-11-17: Keizai now havean demo account. Go to keizai.se?lang=en and follow the instructions.