chore(release): prepare v0.13.0-beta (#489)

- Bump version 0.12.0-beta -> 0.13.0-beta (src/vocalinux/version.py)
- README: refresh "What's New" for v0.13.0-beta and bump comparison table
- docs/UPDATE.md: add v0.13.0-beta section and bump checkout example
- SECURITY.md: mark 0.13.x supported, 0.12.x unsupported
- docs/RELEASE_PROCESS.md: add v0.13.0-beta to version history
- web: bump package.json / package-lock.json / page.tsx schema + badge
- web changelog: add v0.13.0-beta entry and refresh dateModified

docs/RELEASE_PROCESS.md

@@ -343,6 +343,7 @@ git push origin v0.5.1-beta
 | 0.10.2-beta | 2026-04-08 | Beta | Non-ASCII text injection, IBus Wayland detection, Pop!_OS deps, code quality refactor |
 | 0.11.0-beta | 2026-05-30 | Beta | Advanced Settings tab, IBus/recognition hardening, installer fixes, distro compatibility |
 | 0.12.0-beta | 2026-06-07 | Beta | Remote API engine, Silero VAD, threading/IBus hardening, settings and installer fixes |
+| 0.13.0-beta | 2026-06-30 | Beta | Guided whisper.cpp model variants, Wayland text-injection reliability, hotplug keyboard support, dictation spacing fix, website docs refresh |
 
 ## Questions?