Everything is open source, you can look through the code and the explorer if you want to dig through things.

It's impossible to know which coins are lost. The only ones we can be 100% sure about are coins sent to known burn addresses. That only amounts to a few thousand. Everything else could be in deep storage.

I see plenty of people awfully keen to fork and help themselves to coins that haven't moved for a while. Their owners may take umbrage.

I think fork is not the way to know the amount of bitcoin supply, because it's just for fixing the system, and if you want to know the bitcoin supply, you can dig it with algorithm code and you'll find out.

The whole thing is a complete mystery to me.  I think I am giving up on Bitcoin.  It's too confusing.  And when I read topics like this it really does my brain.  That is why people are losing trust in Bitcoin.  Two many secretive things.

I am not sure what you are referring to about the missing bitcoins ,missing from whom  but when it comes to unaccessible wallets there is nothing you can do about it,the coins are gone forever and it is not able to detect which accounts are not accessible as most of the early miners are storing their coins in their cold wallet and there is no way you can recover those coins even with a fork because you need the private key for that wallet to get those coins.

Around 4 millions of all BTC is lost on old hard drives, people forgot password, dead computers, ignorance etc... but also those coins are calculated in coinmarketcap. so you need to make real calculation

Yes it is true, even though bitcoin all amounts to 21 million when it's all done in the mine, but on the market there will be no 21 million, because I think some bitcoin may have gone missing because many lost bitcoin purses too, and this can affect expensive yes bitcoin later sometime

I don't know how you came to an idea that forking would help in this issue? It is not possible to detect which one is unaccessible.
But if given the ability to know the real circulating supply of bitcoin, I am expecting a certain price rise.

Thats possible if those 2million bitcoins aare excluded that will cause a major coinburn which will lead to an increase to bitcoin

This will somehow help but there are also people holding bitcoins that are not aware of this fork. I mean, we are not sure that all holders will get this information. Also, there are those who just don't care if a fork like this occurs. I think that's the reality. But still, you have a good point. As of now, all we can do is believe on the estimates from, say, Chainalysis.