I found out a few days ago, that regardless of your permission settings on connectors, Claude auto-mode is able to use them. This violated my expectations, and exposed me to the lethal trifeca of AI agents.
I had received an email from a service provider with a link to a platform I had not heard of before. As I often do to learn about something, I asked Claude: "what can you tell me about [platform.com]"? Claude gave me an answer, and to my astonishment it concluded "the service provider that emailed you at 1:59pm today likely uses [platform] to manage projects.
I did a double take. How could Claude know this? I did have a Fastmail connector, but I was pretty sure I had locked down permissions. I checked Claude's settings and sure enough, all actions under the Fastmail connector were set to "Always ask for permission".

I reported it to Anthropic, thinking it was a bug (and a serious one at that). They responded promptly that this was expected behavior, and indeed when I however over the "Needs Approval" icon the tooltip states: "Claude asks before each use, except in sessions set to Automatically approve".

Why is this a problem? Because the auto mode classifier is not fool proof and email is very sensitive (even read only). An attacker could craft content that would prompt Claude to read a 2FA code from my email and post it to some website. While I'm sure auto mode would block many of those instances, I am not ready to trust it with this.
My preference would be for the "Always Ask" setting to ... always ask for permission! Or for a fourth option to be created: Always ask, except in auto mode.
Until then, I've removed the fastmail connector from Claude :'(.