Fundamentally, are there processes in nature (everything beyond that is not random given a 'seed' + 'process'?) where our understanding of physics say they would be random, even if we 10-100-1e10x'ed the precision and accuracy of our measuring instruments?

My intuition would be to search for processes where the sensing/observation is collapsing the process, thus not being able to formulate the dynamics without the observation happening.

Radioactive decay looks like lack of our capability to understand the processes in the nuclei, rather than the universe clicking with fingers.