Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
I am sorry to bring bad news, but Office 2019 will not run under macOS anymore. Check with Costco if they are willing to provide you with a replacement product.
Office Home 2024 is the most recent one-time purchase license of Office, or Office Home & Business 2024 if you also need Outlook.
Updates from Microsoft in mid July now means that you need an Office version that licenses version 16.83 or later. This excludes Office 2019. You also need macOS 12 or later, but since the computer is new, I guess that your machine meets that requirement already. For more on this, have a look at https://www.brandwares.com/bestpractices/2023/03/most-recent-office-you-can-run-best-practices/ .