No analytics, no telemetry, no usage stats getting shipped home, and no tracking SDK bundled with the app. Two things do leave your Mac. Sparkle asks the appcast whether a newer version exists, and when OpenSolo crashes or hangs it sends a crash report to Sentry (hosted in the EU) so the bug can get fixed.
Crash reports are scrubbed on purpose: a stacktrace and the build number, nothing more. No IP, no username, no breadcrumbs, and never your pane contents, command output, or file paths. They show where the code broke, not what you were doing.