I'm using Android, and this problem seems to have started happening after trying out the CC app suggested by the site; previously, when I tapped the Read Message button from the notification email, the link would open in the Gmail app, then after using the site, I could tap the top left-arrow button (of the parent app, Gmail, not a site button) to exit that sub-browsing session easily and go back to the Gmail email which I could then delete and move on to the next message.
Now, the link either opens in Chrome, or I have to choose which browser to open the link in (since I have two on my phone), if I don't choose "Always" for one of them.
I uninstalled the CC "app" long ago (which I think isn't actually an Android app, because I'm not finding it in the Play Store), but nothing I try gets Gmail to open CC links in itself as a sub-browser session... it's driving me crazy, because now it's many more steps to move on, like I either have to tap Back many times, or close the tab and switch apps, or tap the Recents button on the phone then tap Gmail, which leaves a tab open in Chrome of that browsing session I longer need.
I've gone through settings, app defaults, and cache clearing for Gmail, the Google app, and Chrome, according to online instructions, but CC links just will not open in the Gmail app anymore.
Now I can't find how to install the CC app again to see if I need to disable something in there, or clear it's cache, or hit it with a stick... my thought is that something about that app or how Android handles it has gummed up in-app browsing for Gmail >:-(