Has the rate of papers uploaded to arXiv changed due to Covid-19? I'm wondering how much Covid-19 affected scientific productivity, if it affected productivity negatively at all (c.f. Newton actually did a lot of his most important work while the University of Cambridge was closed due to plague).

I'm using the rate at which papers are published on arXiv as a proxy for "scientific productivity", fully aware that it is not a perfect proxy and probably lags actual productivity by quite a bit. If country-specific statistics are available, e.g. "The number of publications by authors from Italy changed by __% on 9 March 2020, the date the lockdown started", that's even better.
I think it will be interesting to study this 5 years from now, but right now is way too soon.  At least in math, people don’t post papers at a steady, constant rate.  I personally post around 3 papers per year, and most of those represent work that is at least a year old (often much longer than that) by the time I get around to writing it up.  Given what I’ve got partially written right now, I suspect that I will post about the same number (or even a little more) this year, bit that’s just part of the ebb and flow of research.  What is harder to predict is the effect of all this chaos on the production of new math, which won’t be visible for several years.