feat(browser): Mark errors caught in wrap as unhandled

[Lms24]

This PR is part of a series of PRs adjusting the exception mechanism's handled value.

For more details see #8890

Changed Instrumentation

This PR addresses setting the mechanism in the browser package API wrap. I previously didn't know this existed but you live and learn 😅. Decided to keep #8890 atomic and open a separate PR, should we need to revert the changes there.

Note: we should improve the typing of wrap - opened #8897 to track

ref #6073

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser (incl. Tracing, Replay) - Webpack (gzipped)	75.27 KB (+0.06% 🔺)
@sentry/browser (incl. Tracing) - Webpack (gzipped)	31.25 KB (+0.09% 🔺)
@sentry/browser - Webpack (gzipped)	21.86 KB (0%)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (gzipped)	69.8 KB (+0.06% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (gzipped)	28.21 KB (+0.12% 🔺)
@sentry/browser - ES6 CDN Bundle (gzipped)	20.2 KB (+0.06% 🔺)
@sentry/browser (incl. Tracing, Replay) - ES6 CDN Bundle (minified & uncompressed)	220.34 KB (+0.15% 🔺)
@sentry/browser (incl. Tracing) - ES6 CDN Bundle (minified & uncompressed)	85.17 KB (+0.38% 🔺)
@sentry/browser - ES6 CDN Bundle (minified & uncompressed)	59.88 KB (+0.08% 🔺)
@sentry/browser (incl. Tracing) - ES5 CDN Bundle (gzipped)	31.11 KB (+0.12% 🔺)
@sentry/react (incl. Tracing, Replay) - Webpack (gzipped)	75.29 KB (+0.06% 🔺)
@sentry/react - Webpack (gzipped)	21.89 KB (0%)
@sentry/nextjs Client (incl. Tracing, Replay) - Webpack (gzipped)	93.13 KB (+0.06% 🔺)
@sentry/nextjs Client - Webpack (gzipped)	50.8 KB (+0.1% 🔺)

[Lms24]

closing in favour of #8927