feat(core)!: Remove deprecated logger

[AbhiPrasad]

BREAKING CHANGE

In #16901 we deprecated the logger export from @sentry/core.

This PR removes it for the v10 release.

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	23.75 kB	-0.13%	-29 B 🔽
@sentry/browser - with treeshaking flags	22.34 kB	-	-
@sentry/browser (incl. Tracing)	39.62 kB	-0.11%	-42 B 🔽
@sentry/browser (incl. Tracing, Replay)	77.79 kB	-	-
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	67.59 kB	+0.02%	+8 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	82.49 kB	-	-
@sentry/browser (incl. Tracing, Replay, Feedback)	94.59 kB	-	-
@sentry/browser (incl. Feedback)	40.45 kB	-0.06%	-21 B 🔽
@sentry/browser (incl. sendFeedback)	28.43 kB	-0.13%	-36 B 🔽
@sentry/browser (incl. FeedbackAsync)	33.34 kB	-0.06%	-19 B 🔽
@sentry/react	25.5 kB	-0.16%	-40 B 🔽
@sentry/react (incl. Tracing)	41.59 kB	-0.06%	-24 B 🔽
@sentry/vue	28.18 kB	-0.19%	-51 B 🔽
@sentry/vue (incl. Tracing)	41.41 kB	-0.1%	-38 B 🔽
@sentry/svelte	23.78 kB	-0.13%	-29 B 🔽
CDN Bundle	25.18 kB	-	-
CDN Bundle (incl. Tracing)	39.42 kB	-	-
CDN Bundle (incl. Tracing, Replay)	75.41 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback)	80.89 kB	-	-
CDN Bundle - uncompressed	73.44 kB	-	-
CDN Bundle (incl. Tracing) - uncompressed	116.86 kB	-	-
CDN Bundle (incl. Tracing, Replay) - uncompressed	231 kB	-	-
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	243.81 kB	-	-
@sentry/nextjs (client)	43.62 kB	-0.1%	-40 B 🔽
@sentry/sveltekit (client)	40.04 kB	-0.1%	-38 B 🔽
@sentry/node-core	47.24 kB	+0.01%	+1 B 🔺
@sentry/node	143.81 kB	+0.01%	+1 B 🔺
@sentry/node - without tracing	91.31 kB	-	-
@sentry/aws-serverless	102.75 kB	-	-

View base workflow run

[chargome]

LGTM but seems like some of the test applications still import logger?