Is all stdout and stderr passed to Claude?

My playwright tests have a lot of webserver output unless I use --quiet:

[WebServer] 127.0.0.1 - - [27/Jul/2025 07:17:26] "GET /js/mobile-menu.js HTTP/1.1" 200 -
[WebServer] 127.0.0.1 - - [27/Jul/2025 07:17:26] "GET /js/year-selector.js HTTP/1.1" 200 -
[WebServer] 127.0.0.1 - - [27/Jul/2025 07:17:26] "GET /js/share-state.js HTTP/1.1" 304 -
[WebServer] 127.0.0.1 - - [27/Jul/2025 07:17:26] "GET /js/share-utils.js HTTP/1.1" 304 -

When Claude Code runs these tests, is all that stdout passed verbatim to Claude so it counts towards the context? If it is, then I suppose it's important to manage stdout+stderr of commands so Claude only sees output that's actually important.

I have looked around, but haven't been able to find a definitive answer. What I've found:

• https://docs.anthropic.com/en/docs/claude-code/hooks#simple%3A-exit-code
• https://github.com/anthropics/claude-code/issues/2610
• https://github.com/anthropics/claude-code/issues/3884

When asked, Claude Code itself indicated that it did get all stdout and stderr.

edit: Related: https://old.reddit.com/r/ClaudeAI/comments/1l4dmrf/does_terminalstdout_spam_go_into_the_context/