Analysis

Issue #169 reports that saving a WebDAV remote folder with uppercase letters rewrites the path to lowercase. The root cause is sanitizeWebDavRemoteRoot(): it trims and collapses slashes, but also called .toLowerCase(). WebDAV paths are often case-sensitive, so this can point sync/import at a different remote directory.

Issue #383 reports the same mobile WebDAV failure mode when uppercase letters are used: uploads fail after the configured WebDAV path/casing is changed. Preserving the configured root casing fixes that path mismatch.

Issue #178 is the related filename/path safety case for Chinese/Japanese WebDAV book paths. The current client already builds request URLs by percent-encoding path segments; this PR adds regression coverage to keep those Unicode paths in the URL and out of custom request headers.

Changes

• Preserve WebDAV remote root casing while still trimming control characters, outer slashes, and duplicate slashes.
• Update sync store coverage so saved WebDAV configs keep Apps/ReadAny-Sync exactly instead of lowercasing it.
• Add WebDAV client coverage for non-ASCII book paths, verifying the request URL is percent-encoded and the request headers remain ASCII-only auth headers.

Verification

• pnpm exec biome check packages/core/src/sync/webdav-client.ts packages/core/src/sync/webdav-client.test.ts packages/core/src/stores/sync-store.test.ts
• pnpm --filter @readany/core test -- webdav-client sync-store
• pnpm --filter @readany/core test -- sync-files simple-sync webdav-client

Fixes #169
Fixes #383
Fixes #178