Not even talking about stray high-energy particles from distant supernovas and magnetars -- those irradiate ship regardless of its speed.
"Radiation Hazard of Relativistic Interstellar Flight" by Oleg Semyonov: https://arxiv.org/abs/physics/0610030 via Project Rho: https://projectrho.com/public_html/rocket/slowerlight3.php
1mil years is really short in the grand scheme of things.
human brain has 100T synaptic connections. We already have 2 trillion parameter AI models. Parameter count grows more 3x per year. It means that in 4 years we'll have 100T model. My point here is that by the time we have probes to send even to the closest star, the biological brain would be the inferior option, and most probably we'd even be able to upload, just as fun small companions-observers, a bunch of people brains into what by the time would be a superintelligent 100000T+ parameter AI brain of the probe.