fix(web-studio): normalize service worker scope

[ranxi2001]

Description

Studio reused its slashless router base path as the service worker scope. In
the standard /studio/ deployment, browsers therefore rejected
/studio/service-worker.js with scope /studio, and the rejected registration
promise was left unhandled.

This change derives a dedicated slash-terminated scope for service worker
registration while leaving the router base path unchanged. Registration
failures are caught and logged with context.

Human Involvement

• A human participated in the implementation or review loop
• This PR was generated entirely by AI agents without human participation in the loop

Related Issue

Fixes #3959

Type of Change

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation update
• Refactoring (no functional changes)
• Performance improvement
• Test update

Changes Made

• Normalize service worker script URLs and scopes for root and nested deployments.
• Catch and log registration failures instead of leaving a rejected promise unhandled.
• Add focused regression tests for path normalization and registration outcomes.

Testing

• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• I have tested this on the following platforms:
  • Linux
  • macOS
  • Windows

Commands run:

npm test -- src/lib/service-worker.test.ts
npm test
npm run lint
npm exec -- tsc --noEmit --strict --skipLibCheck --target ES2022 --module ESNext --moduleResolution bundler --lib ES2022,DOM src/lib/service-worker.ts
npm run build -- --base=/studio/
npm exec -- prettier --check src/main.tsx src/lib/service-worker.ts src/lib/service-worker.test.ts
git diff --check upstream/main...HEAD

The production /studio/ bundle was also exercised in Playwright Chromium. As
a control, the old { scope: '/studio' } call raised the reported
SecurityError; the patched bundle registered /studio/service-worker.js at
scope /studio/ with no page error.

Checklist

• My code follows the project's coding style
• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• Any dependent changes have been merged and published

Screenshots (if applicable)

Not applicable.

Additional Notes

The repository-wide TypeScript check still reports existing errors in unchanged
source and generated client files. The new helper passes a focused strict
TypeScript check. Repository-wide Prettier also reports three unchanged files;
all files changed by this PR pass Prettier.