What controls visibility for specific catalog or supplier in an SAP variant site?

Supplier visibility starts with purchase organization (Purchase Org) to Supplier mapping before any catalog view restrictions are put in place in the query used for catalog searches. If the Supplier is not mapped to the Purchase Org of the user, the associated catalog or Supplier is hidden.

In Guided buying(GB), in addition to Purchase Org, Supplier visibility is also driven by Purchasing Unit(PU).

Assign the Supplier to the Purchase Org associated with the user who is unable to see the desired Supplier. Configure this using the Import Purchase Organization to Supplier Mapping task (PurchaseOrgSupplierCombo.csv) file which maps the Supplier to all Purchase Org where it should be available for ordering.

For GB, make sure the Supplier is assigned to all the necessary PU where users should have access to the Supplier, especially in cases where you allow users to buy on behalf of other PU's.

Catalog Management > Catalog Search
Catalog Management > Catalog Views/Item Constraints