Why are my revenues recorded according to the billing date and not the payment date?

In the vast majority of cases, your accounting method will require revenue to be recognized according to the date on which the service is rendered and not according to the date of payment. This is known as accrual accounting.

According to the Canada Revenue Agency (https://www.canada.ca/en/revenue-agency/services/tax/businesses/small-businesses-self-employed-income/business-income-tax-reporting/accounting-your-earnings.html): Generally, you have to report business income using the accrual method of accounting. Farmers, fishers, and self-employed commission agents can use the cash method or the accrual method to report income, but not a combination of both... Under the accrual method, you have to report income in the fiscal period you earn it, no matter when you receive it. You can deduct allowable expenses in the fiscal period you incur them, whether or not you pay for them in that period. Incur usually means you paid or will have to pay the expense.