The Markets Home migration should not have directly impacted metaobject definitions, data, or Liquid access. Metaobjects are a data layer, not a publishing/market layer
They sit outside the catalog/publishing infrastructure that was migrated.
The customer_type metaobject references used in their theme templates to conditionally render content should still resolve the same way.
However, if their theme templates reference metaobjects within sections that are now subject to storefront contextualisation overrides, and those overrides aren't properly configured for the B2B market