I don’t think the arrangement of clauses in sentence 1. & 2. has anything to do with how we determine the 2 major classes (coordinating and subordinating) of conjunctions. It’s the type and nature of the actual conjunction itself that determines that.
‘Since’ is typically used as a subordinating conjunction of time (if it means in the course of the period following the time when) or reason (if it means because).
Typical coordinating conjunctions are but, also, or, either … or & some of those as listed by you.
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