I'm a Russian citizen. I've noticed that literally all online EU shops and service providers (e.g. web hosting) add VAT to the price. I've spent some time looking for an article that implicitly states that VAT should be paid by foreign non-EU citizens when shopping or purchasing services online but couldn't find one. What article or articles make this statement?
Let's say I'm in the UK. I order something online in the UK for £120. In reality, the store calculated this as £100 + £20 VAT, and £20 of my £120 will be sent straight to HMRC (UK tax office). Since store and I are both in the UK, that's how they have to do that by law. (There are exceptions, but this is the most common case).
Now you are in Russia. The company is likely not much interested in a few sales to Russia. So they don't have to charge you VAT. But they will sell to you for £120, send you an invoice for £100 + £20 VAT, and send £20 to HMRC. Just as with my purchase. They don't have to do this, but they do, because everything else is much more complicated and not worth the extra work for them, and not worth getting fined if they do it wrong. You can try to get the money back from HMRC - good luck. The store won't help you; they don't have to, and it's extra work.
So in practice your choice is to pay £120 for the item, or to not buy it.
If you ordered 1,000 of these £100 + VAT item, you would likely convince them to do the extra work for a £100,000 sale. Or if you went to a store that sells lots of expensive items to tourists, where these sales make a significant portion of their total sales, and they know how to do this correctly.