I already have a comment on this subject in a thread here but I believe this should be stressed more explicitly.
Apple didn't kill offline web apps. You can always add an interaction to your app which exports the stored data into a file which then can be saved by the user. It can be done entirely on the client side as well. If anything died here, it is the implicit consent by the user for allowing unnoticed storage space consumption. Implementing an export function will automatically make your app portable, which is always appreciated I believe.
Most data on local storage is some kind of structured tree, table or blob. All can be exported with only little effort.
HTML5 games -> Prompt user with a dialog to download saves/assets after they play the game for a while.
Productivity apps -> Detect "ctrl/cmd + s" to prompt a save dialog. Add save buttons somewhere visible.
Map like apps -> Do nothing. If the user is not visiting the map for 7 days, they don't need the map data persisted either. If necessary, allow explicit save with UI buttons for people who travel often.
Apps/sites which use local storage for auth related artifacts -> Notify users if they click "Remember Me" and explain them the caveats. Allow for encrypted save if users ask for it.
Kiosks -> Use Electron or a similar tech.
I am open to counter arguments. I don't have any idea about how mobile browsers behave for the scenarios stated above.
Edit: I use draw.io since last year and the experience there is as refreshing as it can be in this SPA jungle. I use it as a good example to learn from for my own web app projects.