feat(replay): Capture exception when internal_sdk_error client report happens

[billyvg]

We currently have no visibility when this client report happens. Lets capture the exception if our experimental flag is on.

Also refactors _handleException() to be a public method instead of private.

[github-actions]

size-limit report 📦

Path	Size
@sentry/browser	22.45 KB (0%)
@sentry/browser (incl. Tracing)	34.22 KB (0%)
@sentry/browser (incl. Tracing, Replay)	70.26 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	63.59 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing, Replay with Canvas)	74.66 KB (+0.01% 🔺)
@sentry/browser (incl. Tracing, Replay, Feedback)	87.24 KB (0%)
@sentry/browser (incl. Tracing, Replay, Feedback, metrics)	89.08 KB (0%)
@sentry/browser (incl. metrics)	26.75 KB (0%)
@sentry/browser (incl. Feedback)	39.37 KB (0%)
@sentry/browser (incl. sendFeedback)	27.06 KB (0%)
@sentry/browser (incl. FeedbackAsync)	31.7 KB (0%)
@sentry/react	25.22 KB (0%)
@sentry/react (incl. Tracing)	37.22 KB (0%)
@sentry/vue	26.6 KB (0%)
@sentry/vue (incl. Tracing)	36.06 KB (0%)
@sentry/svelte	22.58 KB (0%)
CDN Bundle	23.64 KB (0%)
CDN Bundle (incl. Tracing)	35.88 KB (0%)
CDN Bundle (incl. Tracing, Replay)	70.28 KB (+0.03% 🔺)
CDN Bundle (incl. Tracing, Replay, Feedback)	75.55 KB (+0.02% 🔺)
CDN Bundle - uncompressed	69.37 KB (0%)
CDN Bundle (incl. Tracing) - uncompressed	106.31 KB (0%)
CDN Bundle (incl. Tracing, Replay) - uncompressed	218.08 KB (+0.06% 🔺)
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	230.9 KB (+0.06% 🔺)
@sentry/nextjs (client)	37.08 KB (0%)
@sentry/sveltekit (client)	34.81 KB (0%)
@sentry/node	111.92 KB (0%)
@sentry/node - without tracing	89.33 KB (0%)
@sentry/aws-serverless	98.5 KB (+0.01% 🔺)

[mydea]

let's replace this line instead with the handleException call, I'd say? Otherwise this would double-log as of now (and it probably also makes sense to log/capture this before the await, I think?)