Fix profilerId propagation

[lbloder]

📜 Description

Fixes an issue where the profilerId was incorrectly matched to the transaction when using the OTEL agent. Caused by a missing profilerId that was not propagated from OTEL agent.

💡 Motivation and Context

Fixes #4854

💚 How did you test it?

📝 Checklist

• I added GH Issue ID & Linear ID
• I added tests to verify the changes.
• No new PII added or SDK only sends newly added PII if sendDefaultPII is enabled.
• I updated the docs if needed.
• I updated the wizard if needed.
• Review from the native team if needed.
• No breaking change or entry added to the changelog.
• No breaking change for hybrid SDKs or communicated to hybrid SDKs.

🔮 Next steps

[github-actions]

Performance metrics 🚀

	Plain	With Sentry	Diff
Startup time	284.49 ms	350.43 ms	65.94 ms
Size	1.58 MiB	2.12 MiB	553.10 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
ee747ae	374.71 ms	455.18 ms	80.47 ms
9fbb112	359.71 ms	421.85 ms	62.14 ms
23d6b12	354.10 ms	408.38 ms	54.28 ms
674d437	355.28 ms	504.18 ms	148.90 ms
604a261	380.65 ms	451.27 ms	70.62 ms
3d205d0	352.15 ms	432.53 ms	80.38 ms
ce0a49e	532.00 ms	609.96 ms	77.96 ms
d5a29b6	298.62 ms	391.78 ms	93.16 ms
ee747ae	358.21 ms	389.41 ms	31.20 ms
27d7cf8	306.76 ms	366.66 ms	59.90 ms

App size

Revision	Plain	With Sentry	Diff
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
9fbb112	1.58 MiB	2.11 MiB	539.18 KiB
23d6b12	1.58 MiB	2.10 MiB	532.31 KiB
674d437	1.58 MiB	2.10 MiB	530.94 KiB
604a261	1.58 MiB	2.10 MiB	533.42 KiB
3d205d0	1.58 MiB	2.10 MiB	532.97 KiB
ce0a49e	1.58 MiB	2.10 MiB	532.94 KiB
d5a29b6	1.58 MiB	2.12 MiB	549.37 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
27d7cf8	1.58 MiB	2.12 MiB	549.42 KiB

Previous results on branch: fix/profilerid-in-otel-agent-case

Startup times

Revision	Plain	With Sentry	Diff
b22e8dc	316.08 ms	363.38 ms	47.30 ms
a2dd6a5	300.96 ms	354.86 ms	53.90 ms
6be0836	312.40 ms	357.54 ms	45.14 ms
39e9d9e	284.42 ms	351.30 ms	66.88 ms

App size

Revision	Plain	With Sentry	Diff
b22e8dc	1.58 MiB	2.12 MiB	551.50 KiB
a2dd6a5	1.58 MiB	2.12 MiB	549.43 KiB
6be0836	1.58 MiB	2.12 MiB	553.00 KiB
39e9d9e	1.58 MiB	2.12 MiB	551.55 KiB

[lbloder]

@sentry review

[lbloder]

@cursor review