[exec] Clean up apply-patch tests (#2648)

## Summary
These tests were getting a bit unwieldy, and they're starting to become
load-bearing. Let's clean them up, and get them working solidly so we
can easily expand this harness with new tests.

## Test Plan
- [x] Tests continue to pass

codex-rs/exec/tests/suite/mod.rs

@@ -1,3 +1,4 @@
 // Aggregates all former standalone integration tests as modules.
 mod apply_patch;
+mod common;
 mod sandbox;