Round 13 P1 finding: the Service tier picker rendered `null` as the
displayed `auto` and converted any explicit `auto` selection back to
`null`, so the chat-adapter's truthy guard then omitted `service_tier`
on the wire. For Anthropic the docs distinguish:
- omitting `service_tier` -> provider default
- `service_tier="auto"` -> opts into Priority Tier when available
- `service_tier="standard_only"` -> opts out
Drop the auto -> null conversion so the user's explicit pick reaches
the adapter and the wire reflects it. `null` still means "never set"
and falls through to the provider default; the existing serviceTier
allowlist already includes "auto" everywhere it matters.