Does it persist the loaded information for the remainder of the conversation or does it intelligently cull the context when it's not needed?

This question doesn’t have anything to do with skills per se, this is just about how different agents handle context. I think right now the main way they cull context is by culling noisy tool call output. Skills are basically saved prompts and shouldn’t be that long, so they would probably not be near the top of the list of things to cull.

Claude Code subagents keep their context windows separate from the main agent, sending back only the most relevant context based on the main agent's request.

Each agent will do that differently, but Gemini CLI, for example, lets you save any session with a name so you can continue it later.