Doing it in the same session does save a ton of tokens but I find it's too biased towards its own implementation even if you tell it to use "fresh eyes" or to "act like a code reviewer in a bad mood." Including those strings in your prompt does show some improvement but not nearly as much as making it think from first principles in a fresh instance.
as long as OpenAI and Anthropic keep subsidizing dirt cheap Codex or Claude Code usage, I'll just keep using them as evaluators. The trick is to have a fresh instance doing the reviewing, not the one that did the work.