Hi,
I'm not able to reproduce the problem on my end with HikaShop 4.6.2.
That's actually an improvement we've added to HikaShop in the 4.4.1.
So I'm surprised you're saying it doesn't work on your website with the 4.6.2.
Could you provide a screenshot of the product "VSBC-6862" settings ?
How did you unpublish the product ? With the icon on the products listing, or with the setting of the product edit form, or something else ? If you unpublish a product with a CSV import, then in that case the product's data won't be reindexed automatically, so it could explain the situation.
What do you mean by "The finder component is reindexed manually." ? Normally, the indexing of a product is done automatically by the finder plugin included in HikaShop. Is that plugin not enabled ?