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What the article means is that the bitcoin protocol does not have an official way to burn coins. But if you need to burn coins, you could very well send them to an address you know is inactive and lost manually.

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PoB is to obtain mining power, according to the article. How would transferring BTC to Satoshi confer any kind of mining power? Or what did the person who transferred the BTC gain from it? that’s what I do not understand, what’s the benefit?

One of the earliest examples of proof of burn that I can remember was around 2013 where counterparty was selling the first (?) tokens using the bitcoin network. Their application used an invalid multi-sig address to send your bitcoin to that would effectively burn it as there would never be a private key that could spend it (can't remember the full details here). Addresses that sent money in would then have tokens available to use on their application layer.

I believe this is actually where the term was first coined as well. What it means now I'm not sure, don't follow crypto.

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