Remote Control ignores settings.json effortLevel (resets to medium on Desktop, high on mobile)

Related to (now locked) #51549.

I run a boot-persistent resident Claude Code agent on a homelab server via settings.json with "effortLevel": "low" set explicitly (via a jq patch in a bootstrap script). That works fine for CLI-originated sessions.

But when I connect to that same session via Remote Control from Claude Desktop, effort silently resets to medium, and from the Claude mobile app it resets to high — both ignoring the settings.json default entirely. If I forget to manually reset it after connecting, I end up sending queries at high effort that I explicitly configured to run at low, with no warning that the override happened.

Would really appreciate either:

1. Remote Control sessions inheriting the effortLevel from settings.json instead of resetting to a client-specific default, or
2. A non-interactive way to set effort (e.g. /effort low usable over Remote Control, not just the local interactive picker) so it can at least be re-applied on connect.

Re-upping this since it's a real footgun for anyone using settings.json to pin effort level on a shared/remote session.