Can I control which auth profile is tried first

Yes. Config supports optional metadata for profiles and an ordering per provider (auth.order.<provider>). This does not store secrets; it maps IDs to provider/mode and sets rotation order.
OpenClaw may temporarily skip a profile if it’s in a short cooldown (rate limits/timeouts/auth failures) or a longer disabled state (billing/insufficient credits). To inspect this, run openclaw models status --json and check auth.unusableProfiles. Tuning: auth.cooldowns.billingBackoffHours*.
You can also set a per-agent order override (stored in that agent’s auth-profiles.json) via the CLI:
# Defaults to the configured default agent (omit --agent)
openclaw models auth order get --provider anthropic

# Lock rotation to a single profile (only try this one)
openclaw models auth order set --provider anthropic anthropic:default

# Or set an explicit order (fallback within provider)
openclaw models auth order set --provider anthropic anthropic:work anthropic:default

# Clear override (fall back to config auth.order / round-robin)
openclaw models auth order clear --provider anthropic
To target a specific agent:
openclaw models auth order set --provider anthropic --agent main anthropic:default