feat!: add paid AI editing workflows

[yuto-trd]

Description

• Add server-backed paid AI image generation, image editing, video generation, caption generation/translation, and job recovery workflows.
• Present the workflows in non-modal AI workspaces with model-aware validation, usage estimates, prompt history, and durable account-scoped recovery.
• Add lease-backed extension points for AI job capabilities, element-source handlers, caption codecs, and caption templates.
• Keep generated media, caption metadata, retries, uploads, and shutdown cleanup bounded and durable.

The branch was rewritten onto origin/main as one focused commit. Unrelated changes were removed into independent PRs:

• fix(file-browser): ignore watcher events after disposal #2322 — DirectoryWatcher disposal race.
• fix(agent-host): harden concurrent endpoint lifecycle #2323 — AgentHost endpoint lifecycle.
• refactor(editor)!: make lifecycle ownership explicit #2324 — generic editor, tool, and project lifecycle ownership.

Affected areas

• Beutl.Api: paid AI transport, models, job monitoring, retry, upload, entitlement, and extension registry contracts.
• Beutl.Editor: asynchronous element sources, AI result application, caption codecs/templates, and serialization.
• Beutl: AI workspace UI, account presentation, recovery, import/export, and application shutdown.
• Extension SDK, package lifecycle handling, localization resources, and focused tests.

Breaking changes

• Beutl.Api adds paid AI contracts and revises AI model, request, retry, upload, availability, and job capability APIs.
• IExtensionProvider uses descriptor/lease discovery and exposes ExtensionsChanged; executable extension instances must be retained only through leases.
• IElementAdder uses AddAsync; ElementDescription uses ElementSource and permits handler-defined duration.
• AI result, source-handler, caption codec, and caption template contributions are registered as independent lease-backed capability slots.
• Extension projects using these contracts must reference Beutl.Api and Beutl.Editor and migrate their registrations.

Test plan

• GitHub build, full CPU tests, Vulkan validation tests, format check, and coverage upload passed at 5d114303a.
• dotnet build Beutl.slnx -c Debug --no-restore --nologo — passed locally with 15 existing warnings and 0 errors.
• Focused regression passes include 102 unit tests for AI jobs/models/captions, 15 AI importer tests, 8 element-entry headless tests, 5 video-import headless tests, and 220 public API contract tests.
• The package-tools cancellation race passed its two-test fixture and 20 consecutive focused repetitions.
• GPL/MIT diff scan and git diff --check passed.
• Changed-file dotnet format --verify-no-changes passed; the full-solution check reports only the existing MediaFoundation CA1416 diagnostics locally.
• Final branch audit: one commit and 288 files. The extracted generic lifecycle API work, DirectoryWatcher race fix, AgentHost endpoint lifecycle fix, and CI workflow edits are not present.

Fixed issues

None.