The minimum permissions required by the CRM enrichment for the installation user are:
System Permission:
API Enabled
Object/Field permission:
Account/Lead
Read
Edit - on all HG Insights fields from the managed package (see here what the package installs)
HG Technographic/ HG Firmographic / HG IT Spend / Account Scoring fields
CRUD, View All, Modify All Permission - on objects
Edit - on all associated fields