Dear Luke Grayson,
Good day!!
Apologies for the inconvenience caused and please don’t worry, let’s work together on your concern and move towards a resolution path.
I understand your concern and would like to convey that I have tested the behavior at my end where I noticed IEEE reference styles in my Word application, and I checked the behavior in the latest version of Semi-Annual and Current channel Word application.
Since you are only having MLA and APA reference styles in Word document, I would like to let you know that generally there will be 12 files, which IEEE2006OfficeOnline.xsl is one of them and it comes with the Office 365 apps installation.

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So, I would like to suggest you access the above path in your File Explorer and see whether you are able to see all files as listed above:
In the Windows Search, search for Run and click on it> Enter %appdata%\Microsoft\Bibliography\Style> Click on OK.
If you are displaying with all files, then I would like to suggest you perform Online Repair to the Office apps and restart your device post the Online Repair. Reference: Repair an Office application - Microsoft Support
However, if you can see only two files APA and MLA, then please follow the below steps:
Quit the Word app> Open the File Explorer> Go to the following location C:\Program Files\Microsoft Office\root\Office16\Bibliography\Style > Copy the files> Open the Run app> Enter %appdata%\Microsoft\Bibliography\Style> Click on OK> Now paste the copied files> Restart your PC> Open the Word app and check the outcome.
Appreciate your patience and understanding. Have a great day!!
Best Regards,
Sophia