Office 2024 is a one-time purchase, so it should not require a Microsoft 365 subscription for activation. Microsoft confirms that Office 2024 for Mac is a perpetual license for one Mac.
If the Mac is showing a Microsoft 365 activation prompt, first verify that the Office 2024 purchase was redeemed to the Microsoft account being used on the Mac.
Recommended steps:
Sign in to the Microsoft account used when redeeming Office 2024 and confirm that Office 2024 appears under your products.
Quit Word, Excel, PowerPoint, and the other Office apps.
Uninstall the current Office applications from Finder > Applications. Microsoft documents the Mac uninstall procedure here.
If the apps continue to use the wrong license, run Microsoft's Office License Removal Tool. This removes the existing Office license information from the Mac; you can then sign in again with the account that owns Office 2024.
Reinstall Office using the installation associated with the Office 2024 purchase and sign in with the same Microsoft account used for redemption. Microsoft provides the Office 2024 activation procedure here.
If Office 2024 does not appear in the Microsoft account after the product key was redeemed, the issue is likely with the entitlement/redemption rather than the Mac installation. In that case, Microsoft Support should verify the purchase and license association.
Do not purchase a Microsoft 365 subscription just to activate the Office 2024 license.