Hi, Andrew Dutka
The installer is not actually changing your purchase to Microsoft 365. On Mac, Office 2024 and Microsoft 365 use the same Office apps and installer package. The license detected during activation determines which version you receive.
First, sign in at Services & subscriptions using the Microsoft account used to redeem or purchase Office 2024. Confirm that Office Home 2024 or Office Home & Business 2024 appears there, then select Install beside that product.
After installation, open Word, select Get Started, and sign in using that same Microsoft account. Do not use an old work, school, or Microsoft 365 account.
If Word still activates as Microsoft 365, it is recommended that you:
Sign out of every account in the Office apps.
Close all Office apps.
Run the official Office License Removal Tool.
Restart the Mac, reopen Word, and sign in only with the account holding Office 2024.
Also, avoid installing the apps from the Mac App Store when activating a separately purchased Office 2024 license.