Because the Chrome implementation is implemented server-side.
That feels like a bad idea in my opinion… in my mind it would make sense to wait for Anthropic to address any browser compatibility issues, especially since claude.ai is clearly software that is being regularly worked on.
I can understand quirks for old websites/ones from companies that work very slowly, but this seems strange to me.
Ideally websites should also test with the beta versions of Firefox, Safari, and Chrome to find and report regressions (browser bugs or web spec changes) so they can get fixed before the release breaks your website.
And why should the cross-market context be treated differently?