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I think the auth session creates a HMAC which allows access for a short while, and because of things like WiFi > 4g hand-off... the HMAC includes browser type but not IP/network... and so the link temporarily works for a short while if enough of the identifying factors are similar (also Chrome, etc).
They don't work in Chrome too.
You haven't shared the images, so what you're seeing is that when you're signed into Google within Chrome, your cookies allow you to see the images.
You're not signed into Google in Safari, so you don't see the images there.
No-one else is signed into Google as you in any browser, so no-one else sees the images.
Ultimately... you need to use Google Photos sharing permissions to make them public and then use the public URL to paste into here (test this by viewing the image in the unauthenticated Safari first)... or... upload the images here.