Re: Why have Satoshi's early mined coins an unusual nonce value distribution?

Another thing is that Satoshi included a hidden message referencing The Times newspaper on the genesis block's coinbase timestamp parameter (The Times 03/Jan/2009 Chancellor on brink of second bailout for banks) and never mentioned it.

That message was put in there to give prove no mining was done before that date. So it was there for a purpose. Since Satoshi was very strict about privacy it wouldn't make sense he intentionally created a way to distinguish blocks mined by himself.

I never hear/don't remember about this, can you show relevant source about it?

You could simply deduct that by reason. If you want to proof something didn't exist before a certain date nowadays you would name something like the hash of a block. You can be pretty sure if you see the correct hash of block 701000 mentioned in a message that message couldn't have been constructed before the block was mined. Satoshi proofed this by quoting the headline of a newspaper. So this genesis block couldn't be mined before the newspaper came out.

A quick google search for "Satoshi pre-mine" turned on some results like https://danhedl.medium.com/bitcoins-distribution-was-fair-e2ef7bbbc892. But then again I don't know the definition you have for relevant source