Feature Request: Add Browser Extension Sync

### Describe the feature you'd like to request

Add extension syncing to Floccus, similar to bookmark sync.

**Problem:**

Privacy-focused browsers (Helium, Ungoogled Chromium) don't have built-in sync. Manually installing 10-20 extensions on each browser is tedious.

**Inspiration:**

[Extension Sync](https://chromewebstore.google.com/detail/kimbiihomiiklblgkdllffbakadjgako) does this via GitHub, but it's limited (2.5★ rating, GitHub-only, no WebDAV/Nextcloud).

**Why Floccus?**

- Already has sync infrastructure (WebDAV/Nextcloud)
- Privacy-focused, open-source
- Cross-browser support exists

### Describe the solution you'd like

**MVP: Extension List Sync**
Sync extension metadata (ID, name, version, enabled state) as JSON:
```json
{
"extensions": [
{
"id": "cjpalhdlnbpafiamejdnhcphjbkeiagm",
"name": "uBlock Origin",
"version": "1.56.0",
"enabled": true,
"url": "https://chrome.google.com/webstore/detail/cjpalhdlnbpafiamejdnhcphjbkeiagm"
}
]
}

User Flow:

1. Enable "Extension Sync" in settings
2. Floccus syncs extension list to WebDAV/Nextcloud
3. On another browser: notification "5 new extensions available"
4. User clicks "Install" → Floccus opens Chrome Web Store tabs
5. User clicks "Add to Chrome" on each tab.

Technical:

- Use chrome.management.getAll() API
- Reuse existing sync infrastructure
- Store as JSON alongside bookmarks

### Describe alternatives you've considered

**Alternatives:**

1. **Extension Sync** - GitHub-only, low rating (2.5★), no WebDAV
2. **Manual install** - Time-consuming, error-prone
3. **Browser sync** - Not available in privacy browsers, requires Google/Mozilla account
4. **Script copying** - Fragile, no cross-device sync

**Why Floccus is better:**
- Self-hosted (WebDAV/Nextcloud)
- Open source
- Already trusted (7,974★)
- No vendor lock-in

**Target users:** Privacy-conscious users, multi-browser users, developers
**Benefit:** Unique feature, no competitor has self-hosted extension sync

Start by locating Floccus's existing bookmark sync flow and its WebDAV/Nextcloud storage path, then review how the browser extension exposes chrome.management.getAll across supported browsers. Define the JSON metadata and user flow alongside bookmarks; done means extension lists can sync and users receive actionable installation prompts without disrupting bookmark sync.

Written by the indexing model from the issue text.