fix(extension): avoid fetching nonexistent overlay CSS

[KennyMcSimpson]

Summary

Fixes #398.

The overlay CSS is already imported with ?inline and supplied to createShadowRootUi. Setting cssInjectionMode: "ui" also makes WXT request content-scripts/content.css, which the production build does not emit.

Remove that setting and keep the existing inline stylesheet. The overlay continues to mount inside its ShadowRoot without the extra request.

Validation

• pnpm ext:test: 2,421 passed, 122 skipped.
• Extension production build and pnpm --filter @browser-skill/extension compile passed.
• pnpm lint passed, including the plugin's 446 tests.
• Executed the actual before/after production content-script bundles in Happy DOM with Chrome API stubs. The old bundle requested the missing CSS once; the updated bundle made no such request. Both mounted the recording controls and the same 32,322 characters of ShadowRoot CSS. Neither manifest added page-level content-script CSS.

A live Chrome smoke test could not run because this environment rejects Chrome's process-singleton socket creation. The bundle check does not cover browser rendering.