How to handle periods at work where projects dry up?

A trait of a senior engineer is being able to define work for themselves. It doesn't have to be (and probably shouldn't be, in your case as a mid-level engineer) some multi-month effort that requires lots of buy-in. Some ideas:

• Could you look at the 50 most recent bug reports and categorize them with root causes?
• Can you look at the incident reports from the last 10 on-call weeks and figure out patterns to make the reports better?
• Can you build a debug tool to make life easier for other engineers?
• Can you stalk a more senior engineer and see where their time is going, and help to accelerate their work? In most healthy cultures, people will be happy to accept the help.

If you're on a team where this is impossible, it's going to be much harder to grow. You want to be in a company where there are more problems than there are people. Problems create opportunities for growth.

I agree with Rahul here. When I was working in Facebook (2011-2017), there was a lot of growth, but even with that, some projects in backend engineers "seemed to dry up", especially when people were busy fighting fires. Good engineers tended to dig into the fires and operational work and find the patters and root cause them. And define work for themselves. I have seen many promotions with such projects.

Define your own work.