These all use the pspReference from the payment, not the store ID.
POST /woocommerce/adyen/payments/{psp_reference}/captures
Body:
{ "amount": { "currency": "EUR", "value": 2800 } }
Authorise vs capture, in plain words: when a payment is authorised, the money is reserved but not actually moved. Capturing is what pulls the money in. Many setups capture automatically, but if yours is set to manual capture you must call this, for example when you ship the goods. You can capture the full amount or a smaller part.
POST /woocommerce/adyen/payments/{psp_reference}/refunds
Body:
{ "amount": { "currency": "EUR", "value": 5000 } }
Gives money back to the shopper. Can be full or partial.
POST /woocommerce/adyen/payments/{psp_reference}/cancels
Cancels a payment that was authorised but not yet captured. No body needed. Use this to release a reservation you are not going to charge (for example an order that fell through before shipping).