TWINT, the Cumulus card can NOT be stored as a customer card (similar to the Coop Supercard)! It is only possible to store the TWINT payment mode in the Migros app under "Pay with the app", just as you can store the Migros bank account, Mastercard, Visa, PostFinance and American Express cards, as well as Migros gift cards... But I suspect this is not the procedure you are looking for.... are indeed two pairs of shoes ;-)

Thanks for your answer, but it's not really the solution paragraph. A more customer-friendly method would be to deposit the card in the same way as Coop.

I also don't understand why this is the case. On the one hand, the TWINT QR code is offered on the display for payment with a smartphone, but on the other hand, you have to get out your Cumulus card beforehand or switch between the Migros app and the TWINT app. I'm also one of those people who generally don't store credit/debit cards or TWINT in any apps.
There is certainly a reason why each bank has its own TWINT app for its debit accounts and banks that don't have their own TWINT app have to use the prepaid TWINT app. Of course, I would have no qualms about using the "Pay with the M app" function to store Migros gift cards there. Personally, I would even welcome it if you could transfer the "Blue Vouchers" there and use them to pay the exact amount.... but this is of course wishful thinking.

Migros is always a bit behind.