Go into Mercury site on nightly, add an announcement, click on shopping card, pick a tool and see it successfully is installed. Pretty simple since TsugiCloud is already installed.
It turns out the issue in SAK-34032 was also present in the shopping cart in the rich text editor. The sakai.session value needs to be added to these return URLs as well.
Add Property to Always Allow sakai.sesson on certain URIs
Adjust ContentItem Implementation to Work with SameSite strict