Solved
I solved the problem thanks to a post on Reddit. For anyone else searching, here's the answer:
One of the recent Zoom updates turned on an option called "Merge Meetings and Calendar tabs". If this option is enabled, the next upcoming meeting isn't shown on the Home tab. I turned the option off and now once again I get the next upcoming meeting shown on the Home tab.
You can only edit the option from the Zoom web site; you then have to quit Zoom and restart it.
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