feat: Add debug logging for the initial props that posthog was started with

[robbie-c]

Changes

I'm debugging things for this customer: https://posthog.slack.com/archives/C05LJK1N3CP/p1720719062387739

I've established that the cross domain cookie is being successfully read from on the second site, but that we are ignoring the values. I'm hoping this extra debugging will help

Checklist

• Tests for new code (see advice on the tests we use)
• Accounted for the impact of any changes across different browsers
• Accounted for backwards compatibility of any changes (no breaking changes in posthog-js!)

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Name	Status	Preview	Updated (UTC)
posthog-js	✅ Ready (Inspect)	Visit Preview	Aug 1, 2024 0:32am

[github-actions]

Size Change: +436 B (+0.04%)

Total Size: 1.16 MB

Filename	Size	Change
dist/array.full.js	333 kB	+109 B (+0.03%)
dist/array.js	154 kB	+109 B (+0.07%)
dist/main.js	154 kB	+109 B (+0.07%)
dist/module.js	154 kB	+109 B (+0.07%)

ℹ️ View Unchanged

Filename	Size
dist/exception-autocapture.js	10.4 kB
dist/recorder-v2.js	110 kB
dist/recorder.js	110 kB
dist/surveys-preview.js	59.5 kB
dist/surveys.js	65.6 kB
dist/tracing-headers.js	8.26 kB
dist/web-vitals.js	5.79 kB

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