Service Appointments in Salesforce Field Service (SFS) are shared with the FIELD_SERVICE_Default public group when the Service Appointment is scheduled to a Service Resource who does not have a Primary Service Territory Membership active during the scheduled time.
The managed package territory sharing solution shares a Service Appointment — when it is scheduled to a Service Resource — with the relevant Service Territory of the resource. This is based on the Service Territory Member Primary or Relocation records, and it allows personas that manage the resource schedule to view all relevant Service Appointments. If no specific Service Territory Member record exists between the Scheduled Start and Scheduled End times of the Service Appointment, the record is shared with the FIELD_SERVICE_Default public group.
Ensure that the Service Territory Member record starts earlier than the working hours start time and ends after the working hours end time for the resource.
If the above configuration does not resolve the issue, disable Service Territory Sharing under Field Service Settings → Sharing → Scheduled Jobs → uncheck "Enable User Territories sharing". Then create custom sharing rules to match the required sharing behavior.
Field Service Sharing Overview
https://help.salesforce.com/s/articleView?id=sf.fs_sharing.htm&type=5
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