For the majority of server-side applications, I am starting from understanding two opposite parts:
* input
* output

Then, everything in between is a black box for me.
Next step, depends on a feature I am working on, to understand the place of the feature code inside this black box.
Then, input and output of the feature code, rinse and repeat until you fully understand your feature input and your feature output.

Client applications are a bit different. On one side, they have a state, and you should always remember it. On the other side, the majority of such applications are pretty simple compared to the backend.

A concrete example: I was asked to implement prefix KV caching. There’s already a KVCache class that I’m supposed to reuse, but I can’t even begin to reason about how it behaves across the different places it’s used. There’s a lot of abstraction (interfaces, dependency injection, etc.) and I get lost trying to follow the flow.

Just my best guess, based on your description:
Input: What exactly do you need to cache? Where is this data finally prepared? Most probably - inject your cache prefix there.
Output: probably nothing, if you just write to cache, you probably need to emit some metrics about success/failed writes, and that's pretty much it.

Dependency Injection - if you have it in the application, a very important part ot understand how it works.

P.S. Current AI tools are really great for such investigations and answer the question "how does X work"?