My advice would be to look at a 101 awesome science tricks for kids type book and see if anything looks useful. Also research on Tesla, Edison, Newton, DaVinci... Certainly steam engines and probably some electricity generation could be made with sufficient manufacturing skills. A lot of it depends on the available materials. Presumably they would have copper.

Definitely calculations relating to navigation and projectile motion could be done. That could give someone a distinct advantage in some scenarios.

There is also medical stuff like ibuprofen from willow bark or penicillin from bread mould.

Degreed.
Audiobook version would work better for me in getting familiar with your world, but I'll have a look.

That's very true, I'll echo the episode of the new Cosmos, regarding the major advancements that happened once they actually had proper refined glass for making telescopes and microscopes.

Finished reading the trilogy. Can't really see a way to critique it without spoiling, but I enjoyed it. I had several sessions of, "can't put it down, sleep can wait."

Here's just a few on topic things that pop to mind as I type them:

If you can make plate armor, you can make steam engines. That might explode at any moment.

Drawing metals into wire can help with mastering electricity. Generators, wet cell batteries, capacitors, etc.

Heavier than air flying machines seem obvious, presuming a high-specific energy fuel source and engine. Airships are low tech. Submarines as well, it's keeping the crew alive that's the problem.