The wording is ambiguous but empirically when I last ran claude -p as part of a job it drew from my $200 API credit.
Not for me, it uses subscription quota.
Interesting could be a bug on my end. I'll look and see if it's a problem with how I set up my sandboxes, or something related to the precedence when both are available in the environment. With all the back and forth on their messaging at the time I took it as a cue to remove the Claude Code dependency from my workflow and start using other providers' models more.
That was almost certainly my problem. If there was a warning about this I could have missed it.
Weirdly I know for sure there was an article behind that first link earlier today but now it's showing no body, just the update boxes. The second doc link is quite clear though.