I occasionally update my web log, however updates are rare because writing ends up taking a lot of time. You have to identify an interesting topic, research it to fill the gaps needed to describe it, create a writeup with associated figures/pictures, edit it, and then commit to publishing it. Yes, it's entirely possible to create lower effort content, but it's substantially less satisfying to me.
Find a small project that you're interested in and check out the developmental discussion channels to see if there's any way you can lend a hand. Starting with trying to find complex coding tasks in large bureaucratic projects is setting yourself up for failure IMO.
For example, https://zynaddsubfx.sourceforge.io/contribute.html shows a few different levels of involvement in one project I maintain. That's not me saying you should work on this project specifically though; you'll want to find projects that you're enthusiastic to learn about.
Usually it takes a few days for the thread to completely populate, so unless you're looking at the rate that it fills up I think it's too early to decide.
No, I would not work on any personal projects during work hours as I don't want to risk any IP clauses getting applied to my own personal/side projects. Generally down time is a good opportunity to learn more about tools which could be applied in the future, but are not immediately required.
You're not (likely) going to be working casually on VLSI design, but for basic circuitry and embedded design you can work on hobby projects. I wouldn't compare that to having a fulltime job working on complex systems where you're going to be exposed to more elaborate challenges, but you can at least avoid letting hardware skills atrophy over time by using them for comparatively simple tasks.