Regarding the sin unto death:
As I believe you have correctly pointed out, it isn’t so much a particular sin as much as the situation which leads to death.
Expressed another way for many others,...God the Holy Spirit indwells us to further sanctify us as He grows us in faith.
When we step out of fellowship, i.e. we sin after believing, we fail to be able to perform a good work by His standards.
In God’s Plan, He might have a large number of good works for us to perform in His Plan. Let’s say His Plan has 20 good works to perform in a certain arena of our lives, but we sin, and miss an opportunity to perform a good work. His Plan still has another 19 good works for us to perform, so He still indwells us,..but if we continue to remain out of fellowship, remaining in sin, ...we might find ourselves missing another opportunity. Now there’s 18 more possible good works for us to perform by His Plan.
If this continues, there might even be different situations arising whereby we can still perform good works, but also there might arise a situation where we are running out of courses of action available to perform by His Plan.
If we continue to remain in sin, out of fellowship and fail in that last opportunity, it also becomes a sin unto death. At that point, God might take us home, still sealed by the Holy SPirit, even though we had fallen out of fellowship, but since He does nothing that is good for nothingness, and we cornered ourselves into a situation where we no longer are performing any good by His Plan, then His natural course of action is to remove us from this life by the first death.
There are also other situations involving the sin against the Holy Spirit, which may also qualify as a/the sin unto death for that person.
IMHO, this is how I have understood the term.