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	284.42 ms	351.30 ms	66.88 ms
Size	1.58 MiB	2.12 MiB	551.55 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
27d7cf8	397.90 ms	498.65 ms	100.75 ms
9fbb112	361.43 ms	427.57 ms	66.14 ms
b3d8889	371.33 ms	426.24 ms	54.92 ms
b3d8889	420.46 ms	453.71 ms	33.26 ms
d217708	355.34 ms	381.39 ms	26.05 ms
27d7cf8	314.17 ms	347.00 ms	32.83 ms
ee747ae	396.82 ms	441.67 ms	44.86 ms
3d205d0	352.15 ms	432.53 ms	80.38 ms
85d7417	347.21 ms	394.35 ms	47.15 ms
d5a29b6	298.62 ms	391.78 ms	93.16 ms

App size

Revision	Plain	With Sentry	Diff
27d7cf8	1.58 MiB	2.12 MiB	549.42 KiB
9fbb112	1.58 MiB	2.11 MiB	539.18 KiB
b3d8889	1.58 MiB	2.10 MiB	535.07 KiB
b3d8889	1.58 MiB	2.10 MiB	535.07 KiB
d217708	1.58 MiB	2.10 MiB	532.97 KiB
27d7cf8	1.58 MiB	2.12 MiB	549.42 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
3d205d0	1.58 MiB	2.10 MiB	532.97 KiB
85d7417	1.58 MiB	2.10 MiB	533.44 KiB
d5a29b6	1.58 MiB	2.12 MiB	549.37 KiB

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

Startup times

Revision	Plain	With Sentry	Diff
a2dd6a5	300.96 ms	354.86 ms	53.90 ms
b22e8dc	316.08 ms	363.38 ms	47.30 ms

App size

Revision	Plain	With Sentry	Diff
a2dd6a5	1.58 MiB	2.12 MiB	549.43 KiB
b22e8dc	1.58 MiB	2.12 MiB	551.50 KiB

[lbloder]

@sentry review

[lbloder]

@cursor review

[cursor]

✅ Bugbot reviewed your changes and found no bugs!

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