Ask HN: How to grow skills-wise (eg, dist sys experience) when in a small pond?

It's becoming clear to me that I"m "growing out of" my current role. I work on a small IT team (within a medium-sized IT department) and the work is/was interesting but I've hit the ceiling in terms of technical challenges, and there is somewhat of a culture of micromanagement in the department (e.g., engineers clock their time against specific "tasks"), further hampering the ability try different/new things. We have a few systems that 'talk' to each other but as far as things like message brokers, partitioned data stores, etc., such things are beyond the scope of what I work on today.

I've been reading here on HN about "systems design" interviews, etc. Seems like a catch-22: I know that many employers nowadays will ask systems design questions as part of an interview, but I'm not sure how to present myself as technically competent in that area.

How could I leverage my current role to bolster my skills? Or, If I had to do take on a side project in my spare time (not ideal but if that's what's needed, then OK), what would you suggest?