chore: Clean up profiler interface

[sentrivana]

Description

• drop experimental options if they have a top-level replacement
• remove start_profile_session and stop_profile_session (replaced by start_profile and stop_profile)

There is a continuous_profiling_auto_start experimental option without a top-level replacement. There's also a try_autostart_continuous_profiler function that says it should be deprecated in favor of "auto lifecycle". There is no auto lifecycle as far as I can tell. Or is this referring to lifecycle=trace? Leaving this as is for now...

Issues

Closes #6946

Reminders

• Please add tests to validate your changes, and lint your code using uv run ruff.
• Add GH Issue ID & Linear ID (if applicable)
• PR title should use conventional commit style (feat:, fix:, ref:, meta:)
• For external contributors: CONTRIBUTING.md, Sentry SDK development docs, Discord community

[github-actions]

Codecov Results 📊

✅ 94098 passed | ⏭️ 5209 skipped | Total: 99307 | Pass Rate: 94.75% | Execution Time: 332m 34s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📉 -6334
Passed Tests	📉 -5064
Failed Tests	—
Skipped Tests	📉 -1270

All tests are passing successfully.

❌ Patch coverage is 50.00%. Project has 2284 uncovered lines.
✅ Project coverage is 90.32%. Comparing base (base) to head (head).

Files with missing lines (1)

File	Patch %	Lines
sentry_sdk/profiler/continuous_profiler.py	50.00%	⚠️ 1 Missing

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    89.97%    90.32%    +0.35%
==========================================
  Files          193       185        -8
  Lines        24946     23593     -1353
  Branches      9000      8552      -448
==========================================
+ Hits         22444     21309     -1135
- Misses        2502      2284      -218
- Partials      1435      1379       -56

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