ref(browser/core): Move all log flushing logic into clients

[AbhiPrasad]

I experimented with a bunch of different approaches to register log flushing implementations, but I found the cleanest and most performant solution was to have log flushing logic live in clients.

This refactors the browser client to do that, and adds tests for all of our flushing logic everywhere.

The bundle size increase is not ideal, but I recognize we have no choice.

After this gets merged in, I'll add the console logging integration to core. I'll also add some quick integrations for pino and winston.

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	23.27 KB	+0.84%	+197 B 🔺
@sentry/browser - with treeshaking flags	23.1 KB	+0.95%	+222 B 🔺
@sentry/browser (incl. Tracing)	36.68 KB	+0.53%	+197 B 🔺
@sentry/browser (incl. Tracing, Replay)	73.85 KB	+0.27%	+203 B 🔺
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	67.22 KB	+0.33%	+222 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	78.5 KB	+0.27%	+212 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback)	91.07 KB	+0.23%	+206 B 🔺
@sentry/browser (incl. Feedback)	40.41 KB	+0.51%	+209 B 🔺
@sentry/browser (incl. sendFeedback)	27.9 KB	+0.69%	+193 B 🔺
@sentry/browser (incl. FeedbackAsync)	32.7 KB	+0.62%	+205 B 🔺
@sentry/react	25.08 KB	+0.88%	+222 B 🔺
@sentry/react (incl. Tracing)	38.6 KB	+0.56%	+217 B 🔺
@sentry/vue	27.48 KB	+0.69%	+191 B 🔺
@sentry/vue (incl. Tracing)	38.38 KB	+0.53%	+206 B 🔺
@sentry/svelte	23.3 KB	+0.82%	+193 B 🔺
CDN Bundle	24.51 KB	+0.73%	+181 B 🔺
CDN Bundle (incl. Tracing)	36.69 KB	+0.51%	+190 B 🔺
CDN Bundle (incl. Tracing, Replay)	71.7 KB	+0.25%	+179 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback)	76.88 KB	+0.24%	+183 B 🔺
CDN Bundle - uncompressed	71.44 KB	+0.72%	+521 B 🔺
CDN Bundle (incl. Tracing) - uncompressed	108.62 KB	+0.48%	+521 B 🔺
CDN Bundle (incl. Tracing, Replay) - uncompressed	219.91 KB	+0.24%	+521 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	232.48 KB	+0.22%	+521 B 🔺
@sentry/nextjs (client)	39.89 KB	+0.54%	+219 B 🔺
@sentry/sveltekit (client)	37.1 KB	+0.52%	+193 B 🔺
@sentry/node	142.92 KB	+0.01%	+13 B 🔺
@sentry/node - without tracing	96.12 KB	+0.02%	+13 B 🔺
@sentry/aws-serverless	120.47 KB	+0.02%	+13 B 🔺

View base workflow run

[mydea]

LGTM!