I recently realized that gContactSync (among with other Thunderbird Add-ons) is unfortunately not compatible with Thunderbird 102. Looking for an alternative I came up with the following solution. To enable Google Contacts sync via nativ Thunderbird 102 function you just have to add a new CardDAV address book and use the following address and your Google Username. Please be aware to adopt part of the URL
<firstname.lastname@example.org> with your own Google email address.