[Browser]: Implement new Profiling API spec

[s1gr1d]

Description

Implement spec based on this document: https://www.notion.so/sentry/Continuous-UI-Profiling-SDK-API-Spec-17e8b10e4b5d80c59a40c6e114470934

Deprecations: profilesSampleRate and profilesSampler
New APIs: startProfiler, stopProfiler, profileSessionSampleRate and profileLifecycle

profiling-node PR for reference: #15635

[linear]

JS-815 [Browser]: Implement new Profiling API spec