Gmail forwarding for to Dext with Xero integration

I use Gmail, Apple Mail, Dext and Xero. I want my email automated so invoices that are already paid by Direct Debit or account are automatically forwarded to Dext and archived, while invoices requiring manual payment remain in my inbox with clear labels... (Budget: $30 - $250 AUD, Jobs: Accounting, Automation, Bookkeeping, Email Developer, Email Handling, Email Marketing, PHP, Xero)