fix(browser): Remove browserPerformanceTimeOrigin side-effects

[timfish]

Due to the side-effect, browserPerformanceTimeOrigin ends up in the non-tracing browser bundle.

This change ensures that the code is only included when tracing is in use at a slight cost to the tracing bundles.

[github-actions]

size-limit report 📦

Path	Size	% Change	Change
@sentry/browser	23.01 KB	-0.66%	-155 B 🔽
@sentry/browser - with treeshaking flags	21.71 KB	-0.59%	-130 B 🔽
@sentry/browser (incl. Tracing)	35.68 KB	+0.07%	+24 B 🔺
@sentry/browser (incl. Tracing, Replay)	72.92 KB	+0.03%	+16 B 🔺
@sentry/browser (incl. Tracing, Replay) - with treeshaking flags	63.33 KB	+0.03%	+19 B 🔺
@sentry/browser (incl. Tracing, Replay with Canvas)	77.34 KB	+0.03%	+21 B 🔺
@sentry/browser (incl. Tracing, Replay, Feedback)	89.73 KB	+0.03%	+20 B 🔺
@sentry/browser (incl. Feedback)	39.77 KB	-0.34%	-136 B 🔽
@sentry/browser (incl. sendFeedback)	27.65 KB	-0.44%	-124 B 🔽
@sentry/browser (incl. FeedbackAsync)	32.4 KB	-0.4%	-131 B 🔽
@sentry/react	25.76 KB	-0.47%	-124 B 🔽
@sentry/react (incl. Tracing)	38.53 KB	+0.05%	+19 B 🔺
@sentry/vue	27.26 KB	-0.46%	-128 B 🔽
@sentry/vue (incl. Tracing)	37.54 KB	+0.07%	+25 B 🔺
@sentry/svelte	23.18 KB	-0.56%	-133 B 🔽
CDN Bundle	24.17 KB	-0.38%	-93 B 🔽
CDN Bundle (incl. Tracing)	35.86 KB	+0.14%	+49 B 🔺
CDN Bundle (incl. Tracing, Replay)	70.96 KB	+0.06%	+37 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback)	76.28 KB	+0.09%	+66 B 🔺
CDN Bundle - uncompressed	71.08 KB	-0.34%	-244 B 🔽
CDN Bundle (incl. Tracing) - uncompressed	106.94 KB	+0.15%	+159 B 🔺
CDN Bundle (incl. Tracing, Replay) - uncompressed	221.01 KB	+0.08%	+161 B 🔺
CDN Bundle (incl. Tracing, Replay, Feedback) - uncompressed	234.21 KB	+0.07%	+161 B 🔺
@sentry/nextjs (client)	38.81 KB	+0.07%	+27 B 🔺
@sentry/sveltekit (client)	36.2 KB	+0.06%	+22 B 🔺
@sentry/node	157.86 KB	-0.08%	-124 B 🔽
@sentry/node - without tracing	98.74 KB	-0.13%	-131 B 🔽
@sentry/aws-serverless	126.47 KB	-0.11%	-134 B 🔽

View base workflow run

[timfish]

@mydea or @billyvg do you know why my changes could be causing this Replay test failure with an incorrect segmentId?
https://github.com/getsentry/sentry-javascript/actions/runs/12156896052/job/33901817087?pr=14025#step:6:426

[timfish]

@lforst since this is now a breaking change, can I rebase this PR on top of the v9 branch?

[lforst]

@lforst since this is now a breaking change, can I rebase this PR on top of the v9 branch?

We already cut the v8 branch so the branch to target with breaking changes is now develop.