Structly is a Safari extension. You hit a JSON page; it beautifies the JSON in front of you. That's everything it does.
The extension reads the JSON content of the page you're viewing because it has to — that's how the formatting happens. Nothing leaves your browser. There's no Structly server. There's no telemetry. The only network request is the one Safari was already making to load the page.
Your collapse/expand preferences and theme choice live on your Mac or iPhone. If iCloud Drive is on, they sync between your devices via Apple's CloudKit, in your private database. I have no access to it.
Apple sees the App Store transaction when you install Structly. I see whatever App Store Connect tells me — install counts, country, device class. No identity, no usage, no pages you visited.