You don't need to explicitly convert Sitecore.Tracking.Analytics.Contact to XConnect.Contact as this is done on session end throughwhere data collected by the tracker is converted. You can take a look at the conversion pipelines described here https://doc.sitecore.com/developers/93/sitecore-experience-platform/en/conversion-pipelines.html, which are also responsible for loading existing contacts into tracker.
XConnect.Contact is used to save/load contact data to xConnect as shown on the diagram https://doc.sitecore.com/developers/93/sitecore-experience-platform/en/tracking-and-xconnect.html.
The Sitecore Tracker uses Sitecore.Analytics.Tracking.Contact to track and identify contacts and their interactions during their visit to the CD instance, it does not use the xConnect model. You should use this model if you wish to modify the contact values in session before being saved into xDB.