They don't share context, on purpose. A subagent starts with an empty context window, its own system prompt (your .md file) and only the task text the main agent writes for it. When it's done, only its final message comes back.
That's the point: the subagent can read 40 files and the main conversation only receives a one-page summary. It saves the main context, not total work.
So in your case either:
- let the subagent do the schema digging and have main Claude never read the migrations itself, or
- put the schema summary in a file (
docs/schema.md) and tell the subagent in its .md to read that first.
Your "give the subagent your findings" works too, but then main has to write them all into the task prompt.