Tags are visible only if Tags is added as the first column in the homepage widget.
Steps to Reproduce
Go to a homepage that has a list of records, for example, the itil homepage.
Open any record.
Add a tag by clicking the tag image next to the number.
Save the tag and go back to the homepage.
Personalize the list view on the homepage to add Tags to the list view.
Note that the tag does not show up for the record you added
Navigate to the list view of the table, click the gear icon, and add Tags in the list layout.
Note that the tag is present for that record in the table list view. The issue occurs only on the homepage.
Make Tags field as the first column in the homepage/dashboard list.
For dashboards, enable responsive dashboard as per document.
Related Problem: PRB640314