The errand run with just a watch is almost possible out of the box: Apple Pay handles the paying. What breaks it is the loyalty card - the supermarket bonus card that gets scanned at every visit and lives in an app on the phone you deliberately left at home.
When Apple Wallet is enough
If your store issues a real Wallet pass, add it - Wallet passes sync to the watch, and double-clicking the side button gets you there. Plenty of loyalty programs don't offer one, though, or bury the barcode inside their own iPhone app with no watch app in sight. That's the gap.
Put the barcode itself on the watch
Wrist Codes stores the codes you actually use and shows them on the watch. Add the card once on the iPhone, and then pick your speed on the wrist - they're not exclusive.
A complication on the watch face. The small one is a one-tap door: glance, tap, the barcode is on screen and scannable. The large one shows the barcode already rendered on the face itself - at the checkout, you just turn your wrist.
A Smart Stack widget. Turn the Digital Crown, and the code is there in the stack - rendered and ready to scan without opening anything.
The app itself, for the codes you use less often.
This is a real supermarket workflow: pay with Apple Pay, scan the bonus card from the wrist at the self-checkout camera scanner, walk out - the phone never had to come. (Author's field test: Albert Heijn, bonuskaart, watch only.)
One honest caveat from the app's own FAQ: complications and widgets are snapshots that watchOS refreshes on its own schedule. If you've just edited a code, tap the complication - opening the app always shows the current version.
Free, for iPhone and Apple Watch. iPhone Home Screen widgets included.
FAQ
Can I put a store loyalty card on my Apple Watch?
Yes. If the store issues an Apple Wallet pass, use Wallet. If it doesn't, Wrist Codes stores the barcode and shows it on the watch via complications and widgets.
Can a checkout scanner read a barcode from a watch screen?
Camera-based scanners - the kind at self-checkouts - read screens fine. Older laser-only scanners can struggle with any screen, phone or watch alike.
Why does my complication show an old barcode?
Complications are snapshots refreshed on the system's schedule. Tapping it opens Wrist Codes with the current data; switching watch faces and back also nudges a refresh.