Two practices that are needed for a custom attribute to map into Order Management assuming the attribute has been created on the necessary objects are:
The types must match within reason. The data type of the custom attribute in Order Managementmust match or be compatible with the data type of the corresponding attribute in the external system, such as B2C Commerce or B2B Commerce. For example, if the attribute is a string in B2C Commerce, it must also be a string in Order Management.
The namesmust be an exact match. The name of the custom attribute in Order Management must be exactly the same as the name of the corresponding attribute in the external system, including capitalization and punctuation. For example, if the attribute is named "kitItem" in B2C Commerce, it must also be named
"kitItem" in Order Management.
Verified References: https://documentation.b2c.commercecloud.salesforce.com/DOC2/topic/com.
demandware.dochelp/OrderManagement/Administration/AdminAttrMgrCustomAttributes.html

Three steps that the administrator should take to implement this functionality are:
Create an External Data Sourcepointing to the external system's database. An External Data Source is a type of metadata that defines the connection and authentication information for an external system that stores data outside of Salesforce. The administrator can create an External Data Source using the Lightning Connect OData 2.0 or 4.0 adapters, which support read-only access to data in relational databases.
Create an External Object for each table of accounting data in the external system. An External Object is a type of custom object that maps to a table in an external system. The administrator can create an External Object for each table of accounting data that they want to access from Salesforce, and define its fields and relationships accordingly.
Create an Indirect Lookup field to connect to the Account. An Indirect Lookup field is a type of custom field that links a child External Object record to a parent standard or custom object record. The administrator can create an Indirect Lookup field on the External Object that references the Account object, and specify the external column name and value that match the Account ID.
Verified References: https://help.salesforce.com/s/articleView?id=sf.external_object_overview.
htm&type=5https://help.salesforce.com/s/articleView?id=sf.external_object_relationships.htm&type=5

The integration between B2C Commerce and Order Management is not enabled by default. To activate it, an administrator needs to file a support case with Salesforce and provide the necessary information, such as the B2C Commerce instance URL, the Order Management org ID, and the API user credentials3

Two statements about the Order Summary object that are accurate are:
It does not exist without the original Order object. An Order Summary is a record that represents the financial summary of an order that is received from an external system, such as B2C Commerce or B2B Commerce. An Order Summary has a master-detail relationship to the Order object, which means that it cannot exist without its parent Order record.
It is read-only for financial order data. An Order Summary contains financial order data, such as total amount, tax amount, discount amount, etc., that are populated from the external system when the order is created. These fields are read-only and cannot be edited in Order Management.
Verified Reference: https://help.salesforce.com/s/articleView?id=sf.order_management_order_summary.htm&type=5