The context for every single turn could in theory be nearly 1MB. Since this context is being stored in the repo and constantly changing, after a thousand turns, won't it make just doing a "git checkout" start to be really heavy?
For example, codex-cli stores every single context for a given session in a jsonl file (in .codex). I've easily got that file to hit 4 GB in size, just working for a few days; amusingly, codex-cli would then take many GB of RAM at startup. I ended up writing a script that trims the jsonl history automatically periodically. The latest codex-cli has an optional sqlite store for context state.
My guess is that by "context", Checkpoints doesn't actually mean the contents of the context window, but just distilled reasoning traces, which are more manageable... but still can be pretty large.