Immediately after switching the page, it will work with CSR.
Please reload your browser to see how it works.
Most of the headaches around cookies seem to be around people trying to get them to work with arbitrary user input. Don't do that. Stick with fixed-length alphanumeric ASCII strings (the kind you use for auth tokens) and you'll be fine.
Try going to https://example.com/somepath and entering the following into the browser console:
I get