You are correct, Microsoft Office Home 2024 does not include the Desktop version of Classic Outlook. Office Home & Business 2024 does.
There are three ways to get Classic Outlook:
1 - Buy a Microsoft 365 subscription that includes downloadable Desktop Apps.
This is all plans except "Microsoft 365 Basic" and "Microsoft 365 Business Basic".
For some subscriptions (e.g. MS 365 Family), the default installer does not include Classic Outlook. You have to download and install it separately.
Then configure it to always use Classic Outlook.
https://www.slipstick.com/outlook/classic-outlook-not-new-outlook/
2 - Buy a perpetual license for Office Home & Business 2024 which includes Classic Outlook for Windows Desktop.
https://www.microsoft.com/en-us/microsoft-365/p/office-home-business-2024/cfq7ttc0pbm7
3 - Buy a perpetual license for Classic Outlook for Windows Desktop.
https://www.microsoft.com/en-us/microsoft-365/p/outlook/cfq7ttc0pbmd
None of this applies to Mac. You can only get New Outlook for Mac. No Legacy.