fix(llm): size unknown models and refuse a section that cannot be served

Three defects surfaced while driving the Models page.

A hand-declared model needed an explicit contextWindow and maxTokens,
but a provider listing usually returns ids and nothing else — so the
page happily wrote a profile the adapter then rejected, which took the
whole namespace down silently. Capacities now fall back to the route's
`defaultContextWindow` (262,144) and `defaultMaxTokens` (32,768). Both
are guesses by construction, which is why they are route fields a
deployment corrects once rather than constants buried in the adapter;
the fallback sizes the model and never becomes a per-request cap.

That silent failure was the second defect. A schema-valid profile the
adapter could not serve was stored and only rejected later, disabling
every route in the namespace with nothing said. `dsh-settings` gains an
optional `validate` on registration — a check for what a schema cannot
express — and `llm-pi-ai` refuses an unserviceable section at the write
that produced it. A stored section that fails keeps the namespace's last
good value, as a schema failure already did, so an externally edited
document still cannot strand the owner. The plugin's own last-good
fallback goes with it: nothing reaching it can fail any more.

Third, a model with no reasoning metadata advertised the single level
`off`, which pi-ai translates to *omitting* the reasoning option — the
same request naming no effort produces. Selecting it disabled nothing,
so a provider whose default is to think kept thinking with `off` shown
as selected. Such a model now reports no reasoning capability at all,
which is the seam's way of saying the control is unavailable, and the
per-model `reasoning` flag is gone: without a thinkingLevelMap to spell
levels it could only invent them.

The protocol table narrows to the three a hand-declared route reaches
today, most-reached first so a surface offering a choice defaults to the
one gateways actually speak.

packages/cordis/tool-cordis/src/api-catalog.ts

@@ -2639,7 +2639,7 @@ export const TYPE_API: readonly TypeApiEntry[] = [
   },
   {
     name: 'SettingsRegisterOptions',
-    declaration: 'export interface SettingsRegisterOptions<T> {\n    base?: Partial<T>;\n    applies?: SettingsApplies;\n}',
+    declaration: 'export interface SettingsRegisterOptions<T> {\n    base?: Partial<T>;\n    applies?: SettingsApplies;\n    validate?: (value: T) => void;\n}',
   },
   {
     name: 'SettingsScope',