We have an engine (a custom DirectX 11 engine, not something that's out in public) that has dynamic lighting (including things like vehicles with headlights), maps that have big outdoor spaces and quite detailed geometry and we want a shadow system to improve the visuals. Are there any things out there that talk about how other games implement shadows or in general about ways to add shadows without causing significant performance drain?

You can find a basic implementation here in the old GPU Gems series. And here is a directx 11 specific walk through. More modern, more accurate versions are out there depending on what you need. All of them make performance tradeoffs so you will need to do research on a bunch of methods to pick between them, likely trying several and benchmarking on your specific software.

This one’s a bit older but definitely did the trick for me: https://takinginitiative.net/2011/05/15/directx10-tutorial-10-shadow-mapping/​

note that is has 2 chapters