We have created several custom Rich Text fields to store an Embedded Link to different Salesforce records for easy access. This functionality works on CTAs, Tasks, and Success Plans but does not work on the new 360 People object.
I created a Support case for this issue and was told that this is a known limitation in the new 360 due to on-click edit functionality.
Our use case for the on-click functionality on the People view is to mirror the ability to click a link from Gainsight to access the SFDC Contact record that was lost when we upgraded to Gainsight NXT.