Headcanon/theory. The 'mysterious woman' that sings Spies Are Forever and Coldest Goodbye is Tatiana. It's years later and she's settled in the US. I imagine Curt has likely died in his fight against Chimera at this point and Tatiana is retelling the story to someone else. That's why she seems so genuinely sad when watching the scene play in the moments she's not singing. She knows what happens and exactly how it ends.
You can also use this to brush away some of the stranger parts. Tatiana is tired and just doesn't know certain things so she fills in the gaps.
Tatiana: He was the deadliest man alive.
Listener: How many people did he kill?
Tatiana: What? I don't know. Like 1147.
Listener: Were they other agents?
Tatiana: No, no they were random teenagers or something. Will you please just let me finish the story?
