Having multiple devices plugged into a power strip can be problematic. Especially if the power strip is from a discount "big bin" in a box store.
Power strip is likely cheaply designed, built with low quality components, and poor manufacturing standards. Little or no testing and even fake "certification" stickers.
The printer has its' own power supply and should not have any impact on the PSU.
My thought is that there is some sort of electrical loop that causes a short or other issue when printer attempts to print.
Or simply drags down the power via the power strip to where the PSU "gives up".
= = = =
Update your post to include full system hardware specs and OS information.
Include PSU: make, model, wattage, age, condition (original to build, new, used, refurbished)?
Disk drive(s): make, model, capacity, how full?
Printer: make and model?
Power strip: make, model, specs? Any surge protection?