Are there measurements I can take on my server's power supply to estimate its health?
Broadly speaking, the main sources of failure in PCs power supplies are: electrolytic capacitors, fans and power semiconductors, so it makes sense that your condition monitoring focuses on them:

Electrolytic capacitors: As mentioned in the comments, check for increase in voltage ripple.

Fans: Measure (if you can) fan’s current consumption and rpms.

Power semiconductors: It’s hard to do condition monitoring from input-output measurements only, so if you can check the temperature (as close as possible to the power semiconductor). An increase can point to a degradation of that power semiconductor’s solder layers.