For some AI steps, we send sender/recipient information, subjects and truncated message bodies from a sample of messages (typically between 100 and 300 depending on the step). For instance we use that to find additional groups of emails to archive, suggest filters to skip the inbox and move messages under a label or identify newsletters.
A local tool/BYOK version could definitely make sense. We didn't really consider it initially because we built the tool around a mostly client-side architecture: Gmail API calls happen client-side
The recent "Sign in with ChatGPT" announcement also looks interesting here. In theory we could keep the tool working pretty much as it does today, but let users connect their own ChatGPT account and use their plan for the AI requests instead of us making those requests through our API account. We haven't looked deeply into it yet though.
We don't currently have "zero data retention" enabled. We're using the standard OpenAI API setup, so inputs/outputs may be retained for up to 30 days (for abuse monitoring, and API data isn't used for training by default)
That's a good point though and definitely something we should consider. In your case, would zdr be enough to make you comfortable using something like this, or would you really want it to be local/BYOK?