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Consider a browser extension. Instapaper has one. Also, an iPhone app would be nice so links can be shared and stored from the phone.

On the iPhone, you might be able to get away with a Shortcut rather than a full app.

so it has a PWA that handles the web share API so you can share straight to it, but I'm not sure how that handles on iOS

I like this idea, will see how feasible it is