Not directly. Card payments reach Xero through Stripe's own bank feed.
Your bookkeeper wants every sale in Xero, and you do not want to type them in twice. Before you choose booking software, you need to know what reaches Xero by itself and what you still record by hand.
Card payments reach Xero through Stripe's bank feed, which you connect in Xero. This is what that means day to day.
Card payments you take through Petboost run through your own Stripe account
In Xero, add Stripe as a bank feed under Bank accounts. Xero's guide: central.xero.com/s/article/Stripe-direct-feeds
Xero brings in your Stripe transactions each day for you to reconcile. It runs one way, so nothing flows back into Petboost
Cash and bank transfers are not in the feed, so you record them in Xero yourself
To see what made up a Stripe payout, open Settings, Stripe Payouts in Petboost: card sales, refunds, Stripe processing fees, Petboost booking fees and the net transferred
For your accountant, download a financial-year statement from Billing, under Invoices & Payment, EOFY