It's less that the identity of the PC slowly changes, and more that you give up assigning it a single identity. Instead you pick a point of reference (let's say, the PC as OP bought it), and then you measure how much it changed from then to now.

That's how it works with quantitative logic - you never ask "is this the ship of Theseus?", you ask instead "how much of this entity is the ship of Theseus, as left initially in the Athenian harbour?"

Let’s take the idea of adding a new piece, say a secondary drive. Does that make the computer a new computer? Of course not, that drive belongs to the whole. Does it make it 6/5? Technically not, since you’re just counting the original pieces…

It can't be 6/5=120% - adding a secondary drive makes the computer slightly more different. It must be less than 100%.

Since I'm counting long-term storage as 20%, and it changed halfway (the old drive is still there), I'd argue that now it's 90% of the PC that OP bought. (Of course, those numbers are simply made up, what matters is the reasoning.)

even if said drive becomes integral to your PC by hosting you Linux distro you migrate to. [...] Others say it changed when you left your Windows loving wife over her poor taste in OS.

This adds two interesting bits of complexity:

1. Software is part of the PC. Data as a whole is. As such once you save a single file in a computer, the computer isn't exactly the same as it was before; similarity is now lower than 100%.
2. Relevancy. A drive hosting your system is more important than one not doing it, even if both are being used. Changing the former should count more to decrease similarity than the later.

but to be fair, it’s a thought experiment, not meant to be solved so much as a way to provoke critical thinking.

Yup. It isn't something serious; just some millenniums old talk. As such losing your train of thought is not a big deal, it's part of the fun.