Safety rated filter caps are required by design to fail in a safe way, without short circuit. Furthermore, X and Y caps have little impact on the quality of DC output. If they fail, the PSU can pass RFI out on the AC line, but that won't direct affect your PC.

I had one fail like that on a 90s CRT TV a few years ago. It just filled up the room with stinky smoke and scared the hell out of the people present (it was at a local retro gaming event mind you!). Not me though, I knew that it had to be a mains suppression cap when I saw that the picture wasn't being affected 😜. I desoldered the cap on the spot and retro gaming resumed.

Is it likely that the one in my 425 (if it has one) would fail though? Of course, I don't use it that often, but I certainly want the computer to survive (preferably without smoke 😜 )for at least 5 more years.

My fear has got so bad, that I went from using it every day, to not plugging it in at all in over 3 days.