Similarly, are there any modern benchmarks of the performance impact of pinning programs to a core in Linux? Are we talking <1% or something actually notable for a CPU bound program?

I have read there are some potential security benefits if you were to keep your most exploitable programs (eg web browser) on its own dedicated core.

It's very heavily dependent on what your processes are doing. I've seen extreme cases where the gains of pinning were large (well over 2x when cooperative tasks were pinned to the same core), but thats primarily about preventing the CPU from idling long enough to enter deeper idle states.