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I don't think you're doing anything wrong, I can replicate myself.
Looks to be a limitation of the UI - would definitely be nice to have though, as individually updating inventory variant by variant is a lot more effort :)
That is a good point. I will log a bug for Commerce team to look into that.
In Catalog view, when I select any Product to edit their variant's inventory (selecting from select menu), it is not showing the product variant name or code. Is there something I am missing or how to distinguish them. See full scenario.
Here you can see General Product (Product Type) have 4 General Variants (Variant Type).
When this General Product is selected, I clicked on Inventories in Select Menu. (for ref. below image)
This shows me inventories info (below image), in which I am not able to identify which inventory belongs to which Variant.
Let me know if I am doing something wrong? Because when I select Pricing, it shows me Product Name and Code info columns (see below screenshot)
This is also happing in latest 13 version of commerce. (screenshot is from 12.17.2)