Lazurio overlay: open the prompt draft thread with the Settings default model, not the composer's last model

[immakermatty]

Follow-up to #35/#36, Platform side: Lazurio/LazurioPlatform#178.

The lazurio.prompt.v1 response gains an optional model_preferences list: [{instanceId, model, options}], in order. Today that is codex → GPT 6.1 Sol / reasoningEffort high, then claudeAgent → Opus 5.5 / effort high.

• When the overlay opens the new draft thread, it sets the thread's model selection to the first preference whose provider instance is configured and signed in on this Environment. It still sends nothing.
• If none is usable, it keeps the default and shows a short hint ("the recommended model isn't available here").
• Tests: only Codex signed in, only Claude signed in, both, neither.
• cwd will be the Lazurio Folder root, so the existing "open or add the project whose root is exactly cwd" rule keeps working unchanged.

[immakermatty]

Simpler direction (Matěj, 2026-10-04): the prompt does not carry a model. When the overlay opens a new draft thread from lazurio-prompt, it sets that thread's model selection (instance, model, effort) to the default model configured in T3 Code Settings. It does not inherit the composer's last selection. Nothing is sent, as before. If the default's provider isn't signed in on this Environment, keep the upstream behaviour and show a short hint. Tests: a default is set and differs from the last-used one; no default is set. Platform side: Lazurio/LazurioPlatform#178 (cwd = Lazurio Folder, and the Environment provisions a sensible default).

[immakermatty]

Context (Matěj, 2026-10-04): the Platform keeps the default model current (option (c) in Lazurio/LazurioPlatform#178; root decision 0189, HumanAndMachines/Lazurio#491). This issue stays as described in the last comment:

• a thread opened from lazurio-prompt takes T3 Code's Settings default model;
• the link never carries a model.

Tracked in Mission Control DEV-6644, task 607.