refactor(config): adopt config-loader-facade across the codebase

Issue #1161. Sweeps 127 files to import from
src/config/config-loader-facade.ts instead of unified-config-loader or
utils/config-manager directly.

WRITE callers (32 files): replaced raw saveUnifiedConfig /
mutateUnifiedConfig / updateUnifiedConfig calls with the facade's
cache-coherent wrappers saveConfig / mutateConfig / updateConfig. This
fixes a latent stale-cache window where direct writes through the
underlying loader bypassed the facade's memoization.

READ callers (95 files): mechanical import-path migration only —
function names unchanged because the facade re-exports them. No
behavior change.

Also updated:
- tests/unit/utils/browser/browser-setup.test.ts (DI interface rename)
- src/management/checks/image-analysis-check.ts (dynamic import rename)
- src/web-server/health-service.ts (dynamic require rename)
- src/ccs.ts (path prefix fix from sweep script)

After sweep: zero raw write callers remain outside src/config/. Direct
imports of config-manager remain only for symbols not in the facade
(getConfigPath, getCcsDirSource, etc). Behavior unchanged; full suite
passes 1824/1824.

Out of scope: switching loadOrCreateUnifiedConfig() callers to
getCachedConfig() — needs per-callsite cache-safety analysis. Tracked
as follow-up.

Refs #1161

src/proxy/proxy-daemon-entry.ts

@@ -1,7 +1,7 @@
-import { loadSettings } from '../utils/config-manager';
 import { resolveOpenAICompatProfileConfig } from './profile-router';
 import { OPENAI_COMPAT_PROXY_DEFAULT_PORT } from './proxy-daemon-paths';
 import { startOpenAICompatProxyServer } from './server/proxy-server';
+import { loadSettings } from '../config/config-loader-facade';
 
 interface RuntimeOptions {
   port: number;

src/proxy/proxy-daemon-paths.ts

@@ -1,5 +1,5 @@
 import * as path from 'path';
-import { getCcsDir } from '../utils/config-manager';
+import { getCcsDir } from '../config/config-loader-facade';
 
 export const OPENAI_COMPAT_PROXY_LEGACY_DEFAULT_PORT = 3456;
 export const OPENAI_COMPAT_PROXY_ADAPTIVE_PORT_START = 43_456;

src/proxy/proxy-port-resolver.ts

@@ -1,9 +1,9 @@
-import { loadOrCreateUnifiedConfig } from '../config/unified-config-loader';
 import {
   OPENAI_COMPAT_PROXY_ADAPTIVE_PORT_END,
   OPENAI_COMPAT_PROXY_ADAPTIVE_PORT_START,
   OPENAI_COMPAT_PROXY_LEGACY_DEFAULT_PORT,
 } from './proxy-daemon-paths';
+import { loadOrCreateUnifiedConfig } from '../config/config-loader-facade';
 
 export interface OpenAICompatProxyPortPreference {
   port: number;

src/proxy/request-router.ts

@@ -1,4 +1,3 @@
-import { loadConfigSafe, loadSettings } from '../utils/config-manager';
 import { expandPath } from '../utils/helpers';
 import type { ProxyOpenAIRequest } from './transformers/request-transformer';
 import {
@@ -6,6 +5,7 @@ import {
   type OpenAICompatProxyRoutingConfig,
 } from './routing-config';
 import { resolveOpenAICompatProfileConfig, type OpenAICompatProfileConfig } from './profile-router';
+import { loadConfigSafe, loadSettings } from '../config/config-loader-facade';
 
 export type ProxyRoutingScenario = 'default' | 'background' | 'think' | 'longContext' | 'webSearch';