feat(cli): enhance PostHog event instrumentation with comprehensive properties

[dannysheridan]

Description

Refs: Slack thread about missing PostHog event properties for fern generate --docs

Enhances PostHog CLI event instrumentation to capture more useful data for support and proactive outreach. Also fixes a bug where event properties were being nested incorrectly in the PostHog payload.

Link to Devin run: https://app.devin.ai/sessions/08e71a3193514b8994bf73c7576e16be
Requested by: danny@buildwithfern.com (@dannysheridan)

Changes Made

• Fixed nested properties bug in PostHog managers: Previously, ...event was spread into properties, which included the properties field itself, then ...event.properties was also spread, causing duplicate/nested data. Now explicitly extracts orgId and command instead.

• Added properties to fern generate --docs: preview, instance, instancesCount, apiWorkspacesCount, brokenLinks, strictBrokenLinks, disableTemplates, skipUpload, isCI

• Added properties to fern docs dev: port, backendPort, brokenLinks, bundlePathProvided, forceDownload, apiWorkspacesCount

• Added properties to fern test: hasTestCommand, generationLanguage, apiWorkspacesCount

• Added properties to fern mock: portProvided, apiWorkspacesCount

• Added properties to other commands: fern api update (apiProvided), fern self-update (versionProvided, dryRun), fern login (deviceCode), fern format (ci, apiProvided)

• Updated README.md generator (if applicable) - N/A

Testing

• Unit tests added/updated
• Manual testing completed - Lint checks pass

Human Review Checklist

• Verify the PostHog manager fix (...event → explicit orgId/command) won't break existing analytics dashboards
• Confirm no sensitive data is being sent in the new properties (instance URLs are intentionally included for support purposes)
• Check property naming consistency across commands

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