In my view, lost coins are those that have been proven to be sent to burn addresses[1] (an address from which they cannot ever be retrieved) and therefore no one can say they will "find" the key to those addresses.
Thus, the bitcoins sent to those addresses[2][3] are lost forever*, otherwise they are "possibly lost" coins.
You are correct. From estimation on possibly lost Bitcoin, we have really lost Bitcoin and false estimated lost Bitcoin. We can not identify the exact numbers for both of them. All numbers we have are only estimation but in my opinion it is enough for us to have an overview on the gift we possibly have from possibly lost Bitcoin. I don't think we need to know the exact numbers.
Bitcoin market is volatile and speculative so estimation is enough.
I don't know if there is a service that counts this bitcoins but it will be less than 100K
I think it is much larger than 100k Bitcoin that is a too small number. The inactive Bitcoin with ages from 5years and above is bigger than 100k certainly. It's clear that it is just possibly lost Bitcoin!
Lost coins only make everyone else's coins worth slightly more. Think of it as a donation to everyone.