Analytics/diagnostics: the "Share analytics" option (System Settings → Privacy, also asked during first-boot setup) is a local on/off switch only - as of now it doesn't actually transmit anything anywhere, it just flips a flag pearOS stores locally (in your kdeglobals config). You can turn it off in System Settings → Privacy any time.
Screen Time: app usage time is tracked entirely locally, in a JSON file at ~/.local/share/pearos-settings/screentime.json. It's not uploaded anywhere - it's read back by System Settings to show you your own usage stats, same idea as Screen Time on macOS/iOS.
Crash logs: if the first-boot setup wizard fails, it can optionally upload the failure log to a public paste service (paste.rs or 0x0.st) so you can share a link when reporting the issue - this only happens on that specific failure screen, requires internet, and is meant to be pasted into a GitHub issue/Discord/Reddit report yourself. Nothing else in the setup wizard uploads logs automatically.