If the org is enabled the advanced lookup in modern advanced find, for the lookup type of fields, it will show the "Advanced lookup" link in dropdown

However, some "Primary Key" type lookup fields are not showing "Advanced lookup" link in dropdown. For each entity, there is one "Primary Key" type field.

Those "Primary Key" type lookup fields can show advanced lookup on record form. But those "Primary Key" type lookup fields will not show advanced lookup in modern advanced lookup