Greptile Summary

This PR fixes a long-standing bug where the Control UI model dropdown sent bare model IDs (e.g. gpt-5.2) to sessions.patch, causing the server's parseModelRef() to fall back to the session's current defaultProvider and produce the wrong provider/model pairing.

The fix is well-scoped and internally consistent:

• buildChatModelOptions now uses provider/model as option value attributes, so the <select> change handler passes the full qualified name to the server.
• resolveModelOverrideValue and resolveDefaultModelValue are updated to return the same provider/model format, keeping ?selected state in sync across page refreshes.
• GatewaySessionsDefaults gains the modelProvider field the server was already sending but the client type didn't expose.

Issues found:

• The defaultLabel in renderChatModelSelect now displays Default (openai/gpt-5.2) using the internal provider/model format, while individual options use the human-friendly gpt-5.2 · openai style — a minor cosmetic inconsistency worth aligning.

Confidence Score: 4/5

• Safe to merge — the core logic is correct and addresses the reported root cause; only a cosmetic display inconsistency remains.
• The fix correctly and consistently applies the provider/model format across option values and the two resolver functions. The sessions.patch call will now receive the properly prefixed model ref that parseModelRef() expects. Score is 4 rather than 5 only because the defaultLabel display still exposes the raw provider/model string instead of the user-friendly model · provider format used by the individual options.
• No files require special attention beyond the cosmetic label issue in app-render.helpers.ts line 595.

This is a comment left during a code review.
Path: ui/src/ui/app-render.helpers.ts
Line: 595

Comment:
**Default label shows raw `provider/model` format**

After this fix, `defaultModel` is now a `provider/model` string (e.g. `openai/gpt-5.2`), so the default option label becomes `Default (openai/gpt-5.2)`. The individual option labels use the friendlier `gpt-5.2 · openai` format, creating a visual inconsistency in the dropdown.

Consider extracting the display portion from `defaultModel` for the label, or building a separate display string:

```suggestion
  const defaultLabel = defaultModel
    ? `Default (${defaultModel.includes("/") ? defaultModel.split("/").slice(1).join("/") + " · " + defaultModel.split("/")[0] : defaultModel})`
    : "Default model";
```

Or more readably, look up the matching catalog entry to reuse its label format:

```
const defaultEntry = (state.chatModelCatalog ?? []).find(
  (e) => (e.provider ? `${e.provider}/${e.id}` : e.id) === defaultModel,
);
const defaultLabel = defaultModel
  ? `Default (${defaultEntry ? `${defaultEntry.id} · ${defaultEntry.provider}` : defaultModel})`
  : "Default model";
```

How can I resolve this? If you propose a fix, please make it concise.

_{Last reviewed commit: 5769b05}

Landed via temp rebase onto main.

• Gate: pnpm check && pnpm build && pnpm test && pnpm check:docs
• Land commit: 931c040
• Merge commit: d9fb50e

Thanks @chrishham!