If we follow precedence from other languages, this will require a SyncTokenPolicy, with a caching mechanism, which does the appropriate thing with the sync-token headers. The current thinking is to hand-modify the SDK to add support for this on top of the generated code (returned as part of operation responses).
This also needs a client-level public helper methods for customers to use, to complete the scenario:
ConfigurationClient::UpdateSyncToken(std::string token);
Concept Doc for reference:
https://learn.microsoft.com/en-us/azure/azure-app-configuration/rest-api-consistency
Examples from other SDKs: