Assign status `unhandled` instead of `crashed` to sessions in browser SDK

[Lms24]

Problem Statement

Currently, our SDKs update the session to status crashed if an unhandled error occurs. This status isn't ideal for browser SDKs because unhandled errors don't cause actual browser crashes. The few browser crashes that do occur are so fatal that we can't catch them :P

Solution Brainstorm

Fortunately, we can now send status 'unhandled' instead of 'crashed' so let's do this!

Develop docs specification is still pending: getsentry/sentry-docs#15086

Additional Context

_{Tip: React with 👍 to help prioritize this improvement. Please use comments to provide useful context, avoiding +1 or me too, to help us triage it.}

[linear]

JS-1013

[Lms24]

So, this is still a nice "good first issue" but given the impact this has on self-hosted version support and Sentry-deduced metrics like "crash free sessions (rate)", the impact of this change is likely quite high. Therefore we're currently tending towards only shipping this in a major.