To understand Rare Satoshis, we first need to understand Ordinals (Bitcoin NFTs). This IS NOT a post about NFTs, I promise! However, in the journey to create Bitcoin NFTs, Casey Rodarmor, the creator of ordinals.com discovered a much more interesting and intriguing asset: Rare Satoshis.
When you start your topic with a false statement, it discourages the reader from continuing reading the rest.
There is no such thing as Bitcoin NFT because Bitcoin is not a token creation platform and it is impossible to create any kind of token using the bitcoin smart contracts.
Ordinals is also not part of the Bitcoin protocol which means you are talking about an exploit in the consensus rules that allows people to inject an
arbitrary data into the chain. Then on another completely centralized platform that has nothing to do with Bitcoin they call that arbitrary data an "NFT" and scam people by selling it to them!
Now that we understand how sats are tracked, we can dive into what makes a satoshi rare. There are multiple types of satoshis that have interesting properties. The broader classification includes:
These are all arbitrary and meaningless. Of course you can come up with any crazy classification like calling any coin in a transaction with ID that starts with 0x101 to be rare! That's your choice and if you can get some newbies to follow that arbitrary classification, you get yourself a community that can also be exploited to make money by selling such coins to them at a higher price!
None of it can be called "token" or "tracking sats" though.
Transfering
UTXOs containing rare satoshis can be transferred untouched by simply making sure that the transaction that involves them as input contains an output of identical size and at an identical offset.
Not surprising at all that the rules for transferring is also arbitrary and mostly technobabble to look like rules. The moment you spend a UTXO it stops adhering to the arbitrary classification above and stops being "rare"!

Extra miner revenue
Any of the previous spam attacks on Bitcoin Network has caused similar fee spikes making it difficult for people to use bitcoin and at the same time increase the miner revenue due to the high fees the attackers pay.
It is not new:
https://bitcointalk.org/index.php?topic=1776143.0epic-sat-mined-bitcoin-halving-block-sells-two-million
In other words some idiot who had no understanding of Bitcoin paid a lot of money for garbage!
Such exploits/scams are also not new.