fix: what the batch C review found

- A redirect followed for a custom base URL (quota on) no longer carries
  the user's key or cookies to another origin, as fetch itself does, and
  a private address may redirect to another private one (already counted).
- The admin Test of an Ollama or Vertex AI entry without a URL goes where
  chat sends that entry's key: the environment's own URL variable, for
  Ollama else the local default. The Test of an Ollama Cloud key without
  a URL went to the cloud while chat went to local Ollama.
- Chat saves: each save notes the chat on screen and the order of the
  reads before reading its data. A save read before switching chats no
  longer writes into the chat switched to, and a copy that waited for its
  thumbnail no longer replaces a newer one.
- "Continue without saving" keeps its button when a later auto-save fails,
  and goes away when a new message is sent.
- A screenshot check that was waiting for its image when the user pressed
  Stop stays skipped after the next message.
- MCP History: draw.io's own copy of a diagram (after get_diagram) no
  longer adds an entry without a picture; a change of background is still
  its own version. The tab ignores an edit's answer that arrives after a
  newer AI write loaded.
- Desktop: a deleted preset is not brought back by a failed switch, and a
  request naming no preset does not stop a rollback. An origin keeping
  an access code counts as having settings.
- .env: a quoted value ending in a backslash ("C:\dir\") is read as dotenv
  reads it.
- The tool card no longer crashes on an id that does not turn into text;
  an older Test's success timer no longer ends a newer Test's spinner.
- Tests that passed without their fix now check it.

tests/unit/validate-model-route.test.ts

@@ -6,7 +6,10 @@ import { POST as validateModel } from "@/app/api/validate-model/route"
 import { getAIModel } from "@/lib/ai-providers"
 
 // No saved admin providers
-vi.mock("@/lib/admin/settings", () => ({ loadSettings: () => ({}) }))
+vi.mock("@/lib/admin/settings", () => ({
+    loadSettings: () => ({}),
+    getEnvFallback: (key: string) => process.env[key] ?? null,
+}))
 
 // Every URL is public (no DNS in tests), unless a test says otherwise
 const privateUrls = vi.hoisted(() => ({ all: false }))