Since the Sesami App doesn't handle payments and all the payment flow goes through Shopify.
Our suggestion:
Downpay is a great app that offers native deposit, partial payment, and card on file via Shopify API.
You can capture the rest of the payment from the order page or POS.
Downpay and the Sesami app work pretty well!
Alternatives and Workarounds
You can use variants to define the payment method and mark the deposit or full amount as part of the booking information when the customer purchases it.
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Same as we have exemplified in this Demo Store: ROSE GARDEN BEAUTY SALON
The "remainder/balance" is a separate transaction you will do over Shopify, whether that takes payment in person or sends an invoice.