Why Magento Store Manager writes qty/stock status, but no source assigned?

Store Manager writes qty/stock status, but no source assignment (inventory_source_item) 

Based on Magento recommendations, you need to create custom Source and Stock in order to use this feature. If you do not have any custom source created, Store Manager will not assign it.

Official Documentation Quote:

"

IMPORTANT

Using the Default Stock and the Default Source is highly discouraged because they are a part of the CatalogInventory module, which is now deprecated. It is recommended that you create and use custom stocks and sources instead.

"

Check here for details:

https://experienceleague.adobe.com/en/docs/commerce-admin/inventory/get-started/migrate