Physics

This is a fantastic answer that clearly spells out the assumptions made and the effects of those assumptions. Well done :)

The sci fi fan in me now wonders: assuming you get to 0.95c before it becomes truly problematic, what kind of shielding would you need at the front of your probe(/spacecraft/etc.) to prevent the effect from totally destroying the probe. Like you can't just blast electronics with x-rays and harsher and expect it to run. So there is probably a mass tradeoff here with a big ole block of ablating lead at the front that ablates from radiation spalling?

There's probably a cost optimization curve there -- mass of shielding, travel time, energy cost to accelerate the probe.

Furthermore, there would be a pressure exerted by that radiation that should slow the probe down over time, but the rate of slowing will depend on the mass/cross section/etc.

And of course running into an interstellar proton or such will be somewhat of a high energy event... More shielding, or hypothetical defenses like the bussard ramscoop...