[Epic] #inc-517 Followups

[kahest]

Technical context is available here: https://github.com/getsentry/team-processing-private/issues/38

### [P1] Post Mortem action items
- [ ] https://github.com/getsentry/sentry-native/issues/959
- [ ] https://github.com/getsentry/sentry-native/issues/960

### \[P2] Post Mortem action items
- [ ] https://github.com/getsentry/sentry/issues/66418
- [ ] https://github.com/getsentry/sentry-java/pull/3189
- [ ] https://github.com/getsentry/sentry-native/pull/944

### Later/optional/TBD
- [ ] https://github.com/getsentry/sentry-native/issues/962
- [ ] Add static+dynamic stack usage measures and alerts in CI
- [ ] https://github.com/getsentry/sentry-native/issues/987