Which permissions does pon need — and what happens without them?

pon only asks for what a particular feature genuinely needs, and you grant each permission separately. Without them your list still works — all that is missing is the convenience attached to each one.

• Location, „While Using the App“ — this lets pon recognize which of your stores you are standing in, pull that section to the top and sort it along your route past the shelves. Without location access the list stays in the planning view; you can still sort it yourself.
• Location, „Always“ — only this allows iOS to wake pon at the right moment when you pass one of your stores. If access is set to „While Using the App“, exactly those passing-by reminders stay away.
• Notifications — so that hints reach you without opening pon: the passing-by hint, „… is shopping now“ from a shared list, reminders about shelf life and repurchasing. They also make shared lists noticeably faster: when someone else changes something, pon can receive a silent signal in the background and fetch the change right away — otherwise you only see it the next time you open the app.
• Camera — for the barcode scanner and nothing else.

For everything to do with location, the same holds as everywhere in pon: it is processed solely on your device and never transmitted to us. The stores pon learns along the way stay there too.

You can change every decision at any time in your device settings under Settings → pon. And you don't have to grant everything at once — start with location, that is where most of what pon takes off your hands comes from.