refactor(api): collapse src/api into src/lib/api

The seven remaining src/api/ modules (analysis, azuracast, bandsintown,
coverCache, migration, network, runtimeLogs) were the last IPC-layer files
outside src/lib/api/, where the rest of the FE IPC clients already live. Move
them (+ the colocated coverCache test) into lib/api and repoint every consumer;
relative-up imports in the moved files become the depth-independent @/ alias.

Pure move + import updates — no behavior change. The layering baseline is
regenerated in the same commit: the moved files' pre-existing store/cover edges
are only now caught under lib/, and the cover<->coverCache cycles are the same
edges re-keyed to the new path (E4 shrinks the allowlist later).

src/features/playback/store/promoteStreamCache.test.ts

@@ -22,7 +22,7 @@ vi.mock('@/lib/api/subsonicStreamUrl', () => ({
   buildStreamUrlForServer: (_sid: string, id: string) => `https://mock/stream/${id}`,
 }));
 
-vi.mock('@/api/coverCache', () => ({
+vi.mock('@/lib/api/coverCache', () => ({
   librarySqlServerId: (k: string) => k,
 }));
 

src/features/playback/store/promoteStreamCache.ts

@@ -3,7 +3,7 @@ import type { Track } from '@/lib/media/trackTypes';
 import { invoke } from '@tauri-apps/api/core';
 import { useHotCacheStore } from '@/features/playback/store/hotCacheStore';
 import { getMediaDir } from '@/lib/media/mediaDir';
-import { librarySqlServerId } from '@/api/coverCache';
+import { librarySqlServerId } from '@/lib/api/coverCache';
 import { hasLocalPersistentPlaybackBytes } from '@/store/localPlaybackResolve';
 
 /**