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Seeing this as well. Fix is to go to Settings → Applications, open each site, and add a host with type Edit pointing to your edit domain. That restores the page tree redirect behaviour from CMS 12.
Confirmed, Andre's fix is spot on. Reading EditUrlResolver in the 13.1.0 source: edit URLs are now resolved per application and only built against a host of type Edit, and the subtle bit is that a missing Edit host doesn't drop the redirect, it silently falls back to the current request host, so it just looks like the link stopped working.
With CMS12 I'm in the pagetree and select something under another site's startpage. I'm then redirected to the EditURL of that site.
With CMS13 this does not seem to be the case? Is there an config option to get the old behavior back?