I think these are the relevant API endpoints, payouts should be from the store (in BTC Payer stores are like bank accounts) that the user selects.
Create store on-chain wallet transaction StoreOnChainWallets_CreateOnChainTransaction
https://docs.btcpayserver.org/api/v1/stores/{storeId}/payment-methods/OnChain/{cryptoCode}/wallet/transactions
Pay Lightning Invoice StoreLightningNodeApi_PayInvoice
https://docs.btcpayserver.org/api/v1/stores/{storeId}/lightning/{cryptoCode}/invoices/pay