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	310.13 ms	361.79 ms	51.66 ms
Size	1.58 MiB	2.12 MiB	553.14 KiB

Baseline results on branch: main

Startup times

Revision	Plain	With Sentry	Diff
806307f	357.85 ms	424.64 ms	66.79 ms
ee747ae	554.98 ms	611.50 ms	56.52 ms
17a0955	372.53 ms	446.70 ms	74.17 ms
2124a46	319.19 ms	415.04 ms	95.85 ms
9fbb112	404.51 ms	475.65 ms	71.14 ms
b6702b0	395.86 ms	409.98 ms	14.12 ms
ee747ae	357.79 ms	421.84 ms	64.05 ms
27d7cf8	314.17 ms	347.00 ms	32.83 ms
9fbb112	361.43 ms	427.57 ms	66.14 ms
96449e8	361.30 ms	423.39 ms	62.09 ms

App size

Revision	Plain	With Sentry	Diff
806307f	1.58 MiB	2.10 MiB	533.42 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
17a0955	1.58 MiB	2.10 MiB	533.20 KiB
2124a46	1.58 MiB	2.12 MiB	551.51 KiB
9fbb112	1.58 MiB	2.11 MiB	539.18 KiB
b6702b0	1.58 MiB	2.12 MiB	551.79 KiB
ee747ae	1.58 MiB	2.10 MiB	530.95 KiB
27d7cf8	1.58 MiB	2.12 MiB	549.42 KiB
9fbb112	1.58 MiB	2.11 MiB	539.18 KiB
96449e8	1.58 MiB	2.11 MiB	539.35 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