When owner of a record is changed to another Technician, whether previous owner can track the request status?

Yes. We can enable the setting key - Enable or Disable Owner Change Ticket View. If this setting key is enabled, technician can access the tickets of his ownership changed to another.

Once this option is enabled, when we try to change the owner user will get an option - Enable owner to track this request. Check this check box and change the Owner.

In ticket list/grid view user will get an option to view the list of tickets.

Note: This feature is available only in New UI