Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
I would highly recommend that you turn off the automatic Office updates. I would guess that with the updates for Office 2007 removed by MSFT that you are likely to corrupt the programs by trying to find the patches.
I would see if you can find, download and save the Office SP and then install them manually. You might have problems finding the service patches for old versions of Office. Once support is discontinued years ago and as time goes on MSFT tends to remove the service patches.
Many will argue that because Office 2007 is out of service that you must 'upgrade' to a newer version. I am of the old school that tend to believe that if it ain't broke then don't fix it. I use lots of legacy software and prefer it to the new web-centric versions.
I run 5 versions of Publisher.. I installed SP2 to Pub 2007 which if memory serves also contains the 'fix' that allows me to open newer file versions Publisher. I don't remember why I chose to not install the Office 2007 SP3, but you should be fine installing it. SP3 does include SP1 and SP2. Here is a description: https://support.microsoft.com/en-us/topic/description-of-the-2007-office-suite-sp3-and-of-office-language-pack-2007-sp3-6b035e99-1619-a3c6-427d-fe202b5eda27
Most of these old SPs can still be found in the Microsoft Update Catalog. Here is what seems to be the link to the SP3 for Office 2007. https://www.catalog.update.microsoft.com/Search.aspx?q=2526086
DavidF