Isn't 6 confirmation an outdated method? In most cases, as far as I know, 3 confirmation is a safe bet and some websites even use something like confidence factor where they calculate via some methods the probability of double spend.
There is a rule of thumb saying that it is extremely unlikely for a chain reorg to be 6 blocks deep. The six blocks rule of thumb comes from the math in the white paper and an analysis in a very old post here somewhere.
Has it ever been 5 block deep? 4 block deep? And what will happen if chain reorg will be 6 blocks deep? Will the 6 block criteria just grow or can it turn into a huge problem?
It's at everyone's personal discretion after how many confirmations they deem a Bitcoin transaction as settled. A small online shop will have a different risk profile than a large online exchange. I think most exchanges still require 6 confirmations before allowing trading and withdrawal, while casinos tend to allow gambling after 1 confirmation but require a few more confirmations for withdrawal.
The deepest re-orgs were 53 blocks in 2010 and 24 blocks in 2013:
https://bitcoin.stackexchange.com/questions/92974/what-is-the-length-of-largest-known-reorganization-in-bitcoinI'm not aware of any other major re-orgs happening since then, but back in 2017 during the fork wars, most exchanges highly increased confirmation requirements for the minority forks like Bitcoin Cash. IIRC it was in the order of 24, maybe even as high as 120 confirmations on some exchanges.