feat(browser): Trace continuation from server-timing headers

[github-actions]

Note

The pull request "feat(browser): Trace continuation from server-timing headers" was created by @timfish but did not reference an issue. Therefore this issue was created for better visibility in external tools like Linear.

Currently the only way to propagate trace context from server to browser is via meta tags. In some cases modifying the page HTML can be difficult or have a performance impact.

This PR adds support to the browser SDK to fetch sentry-trace and baggage from the Server Timing header.

[linear]

JS-1393

[github-actions]

A PR closing this issue has just been released 🚀

This issue was referenced by PR #18673, which was included in the 10.39.0 release.