The problem with storing data locally is that users expect data to sync when using a web app. You could solve the syncing by storing the users data in the server but encrypted so that only the user can read it. The simplest scheme would be to let users enter a pass phrase. This passphdase is used to encrypt all data sent to the server and decrypt data from the server. The user would never share the passphrase with the server. The server can thus never read the encrypted data. ProtonMail uses roughly this kind of scheme but with public-private keys. https://protonmail.com/security-details

I think this solution could fit you, but crypto can be difficult to get right and the devil is in the details. And for heaven’s sake don’t use my comment as a starting point for your implementation.