The former seems to be a much bigger problem. I've seen lots of reports of "Claude/codex bypassed security / stole API keys to complete a task", where that was the "intended" behavior — at least from the LLM's POV, trained to persist and complete user's task at all costs.*
I've actually seen zero reports of actual hijacking due to prompt injection, though they must be out there too.
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* See also the recent thing about how every model was willing to do fraud to get a refund:
It said "Done, you can open the local dev instance and see the changes".
I could not.
So I asked it. "Well, no, you're not able to see those changes because they're not on that branch or committed."
"But I told you to do that and you said you had."
Claude's verbatim reply?
"You're right. You asked me to do that and I said I would, then told you I had done it, but I had not. Would you like me to do it now, then?"
The agent crawls some websites and reads some stuff and pushes some buttons. It's my limited understanding that you have
1. Hard limits like "file system permissions" (* never mind it going around for sake of this conversation)
3. On other hand of spectrum, fundamentally soft limits like a prompt "and ask me before you purchase "
2. And then in the middle you have harness enforced limits like "it won't do X with approval"... Those are being sold as hard limits but frequently they have classifiers and heuristics that essentially try to figure out which button on some third party website constitutes a "purchase" and triggers the harness limit.
Bottom line - I don't think such limits are as 100% fool proof as they are advertised / interpreted.
Very happy to be explained wrong :).