After looking around it seems that the issue is not the power supply but rather an issue with the logic board. The symptoms matched everything on this page:
[https://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems/apple-time-capsule-repair/gen4-a1409-issues|https://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems/apple-time-capsule-repair/gen4-a1409-issues]
I did notice upon opening the unit that the fan was very clean (unlike the fans of any of the notebooks I've serviced in my house full of lint/dust/etc.). I don't think the fan has ever worked at all.
During the process of removing the logic board I damaged the fan connector in any case.
I baked the unit in the oven and assembled it back together. It's been half day and the unit seems to be working normally (though feels warm to the touch; not warmer than before leading me to believe the fan has never worked; don't recall every hearing a noise resembling the noise from a fan ever).
Will report if issues reappear.